Options, Futures, and Other Derivatives, 11th Edn by John Hull. All Chapters 1-26. | TEST BANK

Hull: Options, Futures, and Other Derivatives, Eleventh Edition, Global Edition Chapter 1: Introduction Multiple Choice Test Bank: Questions with Answers 1. A one-year forward contract is an agreement where: A. One side has the right to buy an asset for a certain price in one year’s time.

B. One side has the obligation to buy an asset for a certain price in one year’s time.

C. One side has the obligation to buy an asset for a certain price at some time during the next year.

D. One side has the obligation to buy an asset for the market price in one year’s time.

Answer: B A one-year forward contract is an obligation to buy or sell in one year’s time for a predetermined price. By contrast, an option is the right to buy or sell.

2. Which of the following is NOT true?

A. When a CBOE call option on IBM is exercised, IBM issues more stock.

B. An American option can be exercised at any time during its life.

C. A call option will always be exercised at maturity if the underlying asset price is greater than the strike price.

D. A put option will always be exercised at maturity if the strike price is greater than the underlying asset price.

Answer: A When an IBM call option is exercised, the option seller must buy shares in the market to sell to the option buyer. IBM is not involved in any way. Answers B, C, and D are true.

3. A one-year call option on a stock with a strike price of $30 costs $3; a one-year put option on the stock with a strike price of $30 costs $4. Suppose that a trader buys two call options and one put option. The breakeven stock price above which the trader makes a profit is: A. $35 B. $40 C. $30 D. $36 Answer: A When the stock price is $35, the two call options provide a payoff of 2 × (35 − 30) or $10. The put option provides no payoff. The total cost of the options is 2 × 3 + 4 or $10. The stock price in A, $35, is therefore the breakeven stock price above which the position is profitable because it is the price for which the cost of the options equals the payoff.

4. A one-year call option on a stock with a strike price of $30 costs $3; a one-year put option on the stock with a strike price of $30 costs $4. Suppose that a trader buys two call options and one

put option. The breakeven stock price below which the trader makes a profit is: A. $25 B. $28 C. $26 D. $20 Answer: D When the stock price is $20, the two call options provide no payoff. The put option provides a payoff of 30 − 20 or $10. The total cost of the options is 2 × 3 + 4 or $10. The stock price in D, $20, is therefore the breakeven stock price below which the position is profitable because it is the price for which the cost of the options equals the payoff.

5. Which of the following is approximately true when size is measured in terms of the underlying principal amounts or value of the underlying assets?

A. The exchange-traded market is twice as big as the over-the-counter market.

B. The over-the-counter market is twice as big as the exchange-traded market.

C. The exchange-traded market is about ten times as big as the over-the-counter market.

D. The over-the-counter market is about ten times as big as the exchange-traded market.

Answer: D The over-the-counter market is about $600 trillion whereas the exchange-traded market is about $60 trillion.

6. Which of the following best describes the term “spot price”?

A. The price for immediate delivery.

B. The price for delivery at a future time.

C. The price of an asset that has been damaged.

D. The price of renting an asset.

Answer: A The spot price is the price for immediate delivery. The futures or forward price is the price for delivery in the future.

7. Which of the following is true about a long forward contract?

A. The contract becomes more valuable as the price of the asset declines.

B. The contract becomes more valuable as the price of the asset rises.

C. The contract is worth zero if the price of the asset declines after the contract has been entered into.

D. The contract is worth zero if the price of the asset rises after the contract has been entered into.

Answer: B

A long forward contract is an agreement to buy the asset at a predetermined price. The contract becomes more attractive as the market price of the asset rises. The contract is only worth zero when the predetermined price in the forward contract equals the current forward price (as it usually does at the beginning of the contract).

8. An investor sells a futures contract an asset when the futures price is $1,500. Each contract is on 100 units of the asset. The contract is closed out when the futures price is $1,540. Which of the following is true?

A. The investor has made a gain of $4,000.

B. The investor has made a loss of $4,000.

C. The investor has made a gain of $2,000.

D. The investor has made a loss of $2,000.

Answer: B An investor who buys (has a long position) has a gain when a futures price increases. An investor who sells (has a short position) has a loss when a futures price increases.

9. Which of the following describes European options?

A. Sold in Europe B. Priced in Euros C. Exercisable only at maturity D. Calls (there are no European puts) Answer: C European options can be exercised only at maturity. This is in contrast to American options which can be exercised at any time. The term “European” has nothing to do with geographical location, currencies, or whether the option is a call or a put.

10. Which of the following is NOT true?

A. A call option gives the holder the right to buy an asset by a certain date for a certain price.

B. A put option gives the holder the right to sell an asset by a certain date for a certain price.

C. The holder of a call or put option must exercise the right to sell or buy an asset.

D. The holder of a forward contract is obligated to buy or sell an asset.

Answer: C The holder of a call or put option has the right to exercise the option but is not required to do so. A, B, and C are correct.

11. Which of the following is NOT true about call and put options?

A. An American option can be exercised at any time during its life.

B. A European option can only be exercised only on the maturity date.

C. Investors must pay an upfront price (the option premium) for an option contract.

D. The price of a call option increases as the strike price increases.

Answer: D A call option is the option to buy for the strike price. As the strike price increases, this option becomes less attractive and is therefore less valuable. A, B, and C are true.

12. The price of a stock on July 1 is $57. A trader buys 100 call options on the stock with a strike price of $60 when the option price is $2. The options are exercised when the stock price is $65.

The trader’s net profit is: A. $700 B. $500 C. $300 D. $600 Answer: C The payoff from the options is 100 × (65 − 60) or $500. The cost of the options is 2 × 100 or $200. The net profit is therefore 500 − 200 or $300.

13. The price of a stock on February 1 is $124. A trader sells 200 put options on the stock with a strike price of $120 when the option price is $5. The options are exercised when the stock price is $110. The trader’s net profit or loss is: A. Gain of $1,000 B. Loss of $2,000 C. Loss of $2,800 D. Loss of $1,000 Answer: D The payoff that must be made on the options is 200 × (120 − 110) or $2000. The amount received for the options is 5 × 200 or $1000. The net loss is therefore 2000 − 1000 or $1000.

14. The price of a stock on February 1 is $84. A trader buys 200 put options on the stock with a strike price of $90 when the option price is $10. The options are exercised when the stock price is $85. The trader’s net profit or loss is: A. Loss of $1,000 B. Loss of $2,000 C. Gain of $200 D. Gain of $1,000 Answer: A The payoff is 90 − 85 or $5 per option. For 200 options, the payoff is therefore 5 × 200 or $1000.

However, the options cost 10 × 200 or $2000. There is therefore a net loss of $1000.

15. The price of a stock on February 1 is $48. A trader sells 200 put options on the stock with a strike price of $40 when the option price is $2. The options are exercised when the stock price is $39.

The trader’s net profit or loss is: A. Loss of $800 B. Loss of $200 C. Gain of $200 D. Loss of $900 Answer: C The payoff is 40 − 39 or $1 per option. For 200 options, the payoff is therefore 1 × 200 or $200.

However, the premium received by the trader is 2 × 200 or $400. The trader therefore has a net gain of $200.

16. A speculator can choose between buying 100 shares of a stock for $40 per share and buying 1000 European call options on the stock with a strike price of $45 for $4 per option. For second alternative to give a better outcome at the option maturity, the stock price must be above: A. $45 B. $46 C. $55 D. $50 Answer: D When the stock price is $50, the first alternative leads to a position in the stock worth 100 × 50 or $5000. The second alternative leads to a payoff from the options of 1000 × (50 − 45) or $5000. Both alternatives cost $4000. It follows that the alternatives are equally profitable when the stock price is $50. For stock prices above $50, the option alternative is more profitable.

17. A company knows it will have to pay a certain amount of a foreign currency to one of its suppliers in the future. Which of the following is true?

A. A forward contract can be used to lock in the exchange rate.

B. A forward contract will always give a better outcome than an option.

C. An option will always give a better outcome than a forward contract.

D. An option can be used to lock in the exchange rate.

Answer: A A forward contract ensures that the effective exchange rate will equal the current forward exchange rate. An option provides insurance that the exchange rate will not be worse than a certain level, but requires an upfront premium. Options sometimes give a better outcome and sometimes give a worse outcome than forwards.

18. A short forward contract on an asset plus a long position in a European call option on the asset with a strike price equal to the forward price is equivalent to: A. A short position in a call option.

B. A short position in a put option.

C. A long position in a put option.

D. None of the above.

Answer: C Suppose that ST is the final asset price and K is the strike price/forward price. A short forward contract leads to a payoff of K − ST. A long position in a European call option leads to a payoff of max(ST − K, 0). When added together, we see that the total position leads to a payoff of max(0, K − ST), which is the payoff from a long position in a put option. C can also be seen to be true by plotting the payoffs as a function of the final stock price.

19. A trader has a portfolio worth $5 million that mirrors the performance of a stock index. The stock index is currently 1,250. Futures contracts trade on the index with one contract being on 250 times the index. To remove market risk from the portfolio the trader should: A. Buy 16 contracts B. Sell 16 contracts C. Buy 20 contracts D. Sell 20 contracts Answer: B One futures contract protects a portfolio worth 1250 × 250. The number of contracts required is therefore 5,000,000/(1250 × 250) = 16. To remove market risk, we need to gain on the contracts when the market declines. A short futures position is therefore required.

20. Which of the following best describes a central clearing party (CCP)?

A. It is a trader that works for an exchange.

B. It stands between two parties in the over-the-counter market.

C. It is a trader that works for a bank.

D. It helps facilitate futures trades.

Answer: B A central clearing party is a clearing house that stands between two parties in the over-thecounter market. It serves the same purpose as an exchange clearing house.

Hull: Options, Futures, and Other Derivatives, Eleventh Edition, Global Edition Chapter 2: Futures Markets and Central Counterparties Multiple Choice Test Bank: Question with Answers 1. Which of the following is true?

A. Both forward and futures contracts are traded on exchanges.

B. Forward contracts are traded on exchanges, but futures contracts are not.

C. Futures contracts are traded on exchanges, but forward contracts are not.

D. Neither futures contracts nor forward contracts are traded on exchanges.

Answer: C Futures contracts trade only on exchanges. Forward contracts trade only in the over-the-counter market.

2. Which of the following is NOT true?

A. Futures contracts nearly always last longer than forward contracts.

B. Futures contracts are standardized; forward contracts are not.

C. Delivery or final cash settlement usually takes place with forward contracts; the same is not true of futures contracts.

D. Forward contracts usually have one specified delivery date; futures contracts often have a range of delivery dates.

Answer: A Forward contracts often last longer than futures contracts. B, C, and D are true.

3. In the corn futures contract, a number of different types of corn can be delivered (with price adjustments specified by the exchange) and there are a number of different delivery locations. Which of the following is true?

A. This flexibility tends to increase the futures price.

B. This flexibility tends to decrease the futures price.

C. This flexibility may increase and may decrease the futures price.

D. This flexibility has no effect on the futures price.

Answer: B The party with the short position chooses between the alternatives. The alternatives therefore make the futures contract more attractive to the party with the short position. The lower the futures price, the less attractive it is to the party with the short position. The benefit of the alternatives available to the party with the short position is therefore compensated for by the futures price being lower than it would otherwise be.

4. A company enters into a short futures contract to sell 50,000 units of a commodity for 70 cents per unit. The initial margin is $4,000 and the maintenance margin is $3,000. What is the futures price per unit above which there will be a margin call?

A. 78 cents B. 76 cents C. 74 cents D. 72 cents Answer: D There will be a margin call when more than $1,000 has been lost from the margin account so that the balance in the account is below the maintenance margin level. Because the company is short, each one cent rise in the price leads to a loss or 0.01 × 50,000 or $500. A greater than 2 cent rise in the futures price will therefore lead to a margin call. The futures price is currently 70 cents. When the price rises above 72 cents, there will be a margin call.

5. A company enters into a long futures contract to buy 1,000 units of a commodity for $60 per unit. The initial margin is $6,000 and the maintenance margin is $4,000. What futures price will allow $2,000 to be withdrawn from the margin account?

A. $58 B. $62 C. $64 D. $66 Answer: B Amounts in the margin account in excess of the initial margin can be withdrawn. Each $1 increase in the futures price leads to a gain of $1,000. When the futures price increases by $2 the gain will be $2,000 and this can be withdrawn. The futures price is currently $60. The answer is therefore $62.

6. One futures contract is traded where both the long and short parties are closing out existing positions. What is the resultant change in the open interest?

A. No change B. Decrease by one C. Decrease by two D. Increase by one Answer: B The open interest goes down by one. There is one less long position and one less short position.

7. Who initiates delivery in a corn futures contract?

A. B. C. D.

The party with the long position.

The party with the short position.

Either party The exchange Answer: B

The party with the short position initiates delivery by sending a “Notice of Intention to Deliver” to the exchange. The exchange has a procedure for choosing a party with a long position to take delivery.

8. You sell one December futures contracts when the futures price is $1,010 per unit. Each contract is on 100 units and the initial margin per contract that you provide is $2,000. The maintenance margin per contract is $1,500. During the next day, the futures price rises to $1,012 per unit. What is the balance of your margin account at the end of the day?

A. $1,800 B. $3,300 C. $2,200 D. $3,700 Answer: A The price has increased by $2. Because you have a short position you lose 2 × 100 or $200. The balance in the margin account therefore goes down from $2,000 to $1,800.

9. A hedger takes a long position in a futures contract on a commodity on November 1, 2012, to hedge an exposure on March 1, 2013. The initial futures price is $60. On December 31, 2012, the futures price is $61. On March 1, 2013, it is $64. The contract is closed out on March 1, 2013. What gain is recognized in the accounting year January 1 to December 31, 2013? Each contract is on 1,000 units of the commodity.

A. $0 B. $1,000 C. $3,000 D. $4,000 Answer: D Hedge accounting is used. The whole of the gain or loss on the futures is therefore recognized in 2013. None is recognized in 2012. In this case, the gain is $4 per unit or $4,000 in total.

10. A speculator takes a long position in a futures contract on a commodity on November 1, 2012, to hedge an exposure on March 1, 2013. The initial futures price is $60. On December 31, 2012, the futures price is $61. On March 1, 2013, it is $64. The contract is closed out on March 1, 2013. What gain is recognized in the accounting year January 1 to December 31, 2013? Each contract is on 1,000 units of the commodity.

A. B. C. D.

$0 $1,000 $3,000 $4,000 Answer: C

In this case, there is no hedge accounting. Gains or losses are accounted for as they are accrued. The price per unit increases by $3 in 2013. The total gain in 2013 is therefore $3,000.

11. The frequency with which futures margin accounts are adjusted for gains and losses is: A. Daily B. Weekly C. Monthly D. Quarterly Answer: A In futures contracts, margin accounts are adjusted for gains or losses daily.

12. Margin accounts have the effect of: A. Reducing the risk of one party regretting the deal and backing out.

B. Ensuring funds are available to pay traders when they make a profit.

C. Reducing systemic risk due to collapse of futures markets.

D. All of the above.

Answer: D Initial margin requirements dramatically reduce the risk that a party will walk away from a futures contract. As a result, they reduce the risk that the exchange clearing house will not have enough funds to pay profits to traders. Furthermore, if traders are less likely to suffer losses because of counterparty defaults, there is less systemic risk.

13. Which entity in the United States takes primary responsibility for regulating futures market?

A. Federal Reserve Board B. Commodities Futures Trading Commission (CFTC) C. Security and Exchange Commission (SEC) D. US Treasury Answer: B The CFTC has primary responsibility for regulating futures markets.

14. For a futures contract trading in April, the open interest for a June contract, when compared to the open interest for Sept contract, is usually:

A. B. C. D.

Higher Lower The same Equally likely to be higher or lower

Answer: A The contracts which are close to maturity tend to have the highest open interest. However, during the maturity month itself, the open interest declines.

15. Clearing houses are: A. Never used in futures markets and sometimes used in OTC markets.

B. Used in OTC markets, but not in futures markets.

C. Always used in futures markets and sometimes used in OTC markets.

D. Always used in both futures markets and OTC markets.

Answer: C Clearing houses are always used by exchanges trading futures. Increasingly, OTC products are cleared through CCPs, which are a type of clearing house.

16. A haircut of 20% means that: A. A bond with a market value of $100 is considered to be worth $80 when used to satisfy a collateral request.

B. A bond with a face value of $100 is considered to be worth $80 when used to satisfy a collateral request.

C. A bond with a market value of $100 is considered to be worth $83.3 when used to satisfy a collateral request.

D. A bond with a face value of $100 is considered to be worth $83.3 when used to satisfy a collateral request.

Answer: A A haircut is the amount the market price of an asset is reduced by for the purposes of determining its value for collateral purposes. A is therefore correct.

17. With bilateral clearing, the number of agreements between four dealers, who trade with each other, is: A. 12 B. 1 C. 6 D. 2 Answer: C

Suppose the dealers are W, X, Y, and Z. The agreements are between W and X, W and Y, W and Z, X and Y, X and Z, and Y and Z. There are therefore a total of 6 agreements.

18. Which of the following best describes central counterparties?

A. Help market participants to value derivative transactions.

B. Must be used for all OTC derivative transactions.

C. Are used for futures transactions.

D. Perform a similar function to exchange clearing houses.

Answer: D CCPs do for the OTC market what exchange clearing houses do for the exchange-traded market.

The correct answer is therefore D. CCPs must be used for most standard OTC derivatives transactions, but not for all derivatives transactions.

19. Which of the following are cash settled?

A. All futures contracts B. All option contracts C. Futures on commodities D. Futures on stock indices Answer: D Futures on stock indices are usually cash settled. The rest are usually settled by delivery of the underlying assets.

20. A limit order: A. Is an order to trade up to a certain number of futures contracts at a certain price.

B. Is an order that can be executed at a specified price or one more favorable to the investor.

C. Is an order that must be executed within a specified period of time.

D. None of the above.

Answer: B In a limit order, a trader specifies the worst price (from the trader’s perspective) at which the trade can be carried out.

Hull: Options, Futures, and Other Derivatives, Eleventh Edition, Global Edition Chapter 3: Hedging Strategies Using Futures Multiple Choice Test Bank: Questions with Answers 1. The basis is defined as spot minus futures. A trader is hedging the sale of an asset with a short futures position. The basis increases unexpectedly. Which of the following is true?

A. The hedger’s position improves.

B. The hedger’s position worsens.

C. The hedger’s position sometimes worsens and sometimes improves.

D. The hedger’s position stays the same.

Answer: A The price received by the trader is the futures price plus the basis. It follows that the trader’s position improves when the basis increases.

2. Futures contracts trade with every month as a delivery month. A company is hedging the purchase of the underlying asset on June 15. Which futures contract should it use?

A. The June contract B. The July contract C. The May contract D. The August contract Answer: B As a general rule, the futures maturity month should be as close as possible to, but after the month when the asset will be purchased. In this case, the asset will be purchased in June and so the best contract is the July contract.

3. On March 1 a commodity’s spot price is $60 and its August futures price is $59. On July 1, the spot price is $64 and the August futures price is $63.50. A company entered into futures contracts on March 1 to hedge its purchase of the commodity on July 1. It closed out its position on July 1. What is the effective price (after taking account of hedging) paid by the company?

A. $59.50 B. $60.50 C. $61.50 D. $63.50 Answer: A The user of the commodity takes a long futures position. The gain on the futures is 63.50 − 59 or $4.50. The effective paid realized is therefore 64 − 4.50 or $59.50. This can also be calculated as the March 1 futures price (=59) plus the basis on July 1 (=0.50).

4. On March 1 the price of a commodity is $1,000 and the December futures price is $1,015. On November 1, the price is $980 and the December futures price is $981. A producer of the commodity entered into a December futures contracts on March 1 to hedge the sale of the commodity on November 1. It closed out its position on November 1. What is the effective price (after taking account of hedging) received by the company for the commodity?

A. $1,016 B. $1,001 C. $981 D. $1,014 Answer: D The producer of the commodity takes a short futures position. The gain on the futures is 1015 − 981 or $34. The effective price realized is therefore 980 + 34 or $1,014. This can also be calculated as the March 1 futures price (=1015) plus the November 1 basis (=−1).

5. Suppose that the standard deviation of monthly changes in the price of commodity A is $2. The standard deviation of monthly changes in a futures price for a contract on commodity B (which is similar to commodity A) is $3. The correlation between the futures price and the commodity price is 0.9. What hedge ratio should be used when hedging a one month exposure to the price of commodity A? A. 0.60 B. 0.67 C. 1.45 D. 0.90 Answer: A The optimal hedge ratio is 0.9 × (2/3) or 0.6.

6. A company has a $36 million portfolio with a beta of 1.2. The futures price for a contract on an index is 900. Futures contracts on $250 times the index can be traded. What trade is necessary to reduce beta to 0.9?

A. Long 192 contracts B. Short 192 contracts C. Long 48 contracts D. Short 48 contracts Answer: D To reduce the beta by 0.3 we need to short 0.3 × 36,000,000/(900 × 250) or 48 contracts.

7.

A company has a $36 million portfolio with a beta of 1.2. The futures price for a contract on

an index is 900. Futures contracts on $250 times the index can be traded. What trade is necessary to increase beta to 1.8?

A. Long 192 contracts B. Short 192 contracts C. Long 96 contracts D. Short 96 contracts Answer: C To increase beta by 0.6, we need to go long 0.6 × 36,000,000/(900 × 250) or 96 contracts.

8. Which of the following is true?

A. The optimal hedge ratio is the slope of the best fit line when the spot price (on the y-axis) is regressed against the futures price (on the x-axis).

B. The optimal hedge ratio is the slope of the best fit line when the futures price (on the yaxis) is regressed against the spot price (on the x-axis).

C. The optimal hedge ratio is the slope of the best fit line when the change in the spot price (on the y-axis) is regressed against the change in the futures price (on the x-axis).

D. The optimal hedge ratio is the slope of the best fit line when the change in the futures price (on the y-axis) is regressed against the change in the spot price (on the x-axis).

Answer: C The optimal hedge ratio reflects the ratio of movements in the spot price to movements in the futures price.

9. Which of the following describes tailing the hedge?

A. A strategy where the hedge position is increased at the end of the life of the hedge.

B. A strategy where the hedge position is increased at the end of the life of the futures contract.

C. A more exact calculation of the hedge ratio when forward contracts are used for hedging.

D. None of the above.

Answer: D Tailing the hedge is a calculation appropriate when futures are used for hedging. It corrects for daily settlement.

10. A company due to pay a certain amount of a foreign currency in the future decides to hedge with futures contracts. Which of the following best describes the advantage of hedging?

A. It leads to a better exchange rate being paid.

B. It leads to a more predictable exchange rate being paid.

C. It caps the exchange rate that will be paid.

D. It provides a floor for the exchange rate that will be paid.

Answer: B Hedging is designed to reduce risk not increase expected profit. Options can be used to create a cap or floor on the price. Futures attempt to lock in the price.

11. Which of the following best describes the capital asset pricing model?

A. Determines the amount of capital that is needed in particular situations.

B. Is used to determine the price of futures contracts.

C. Relates the return on an asset to the return on a stock index.

D. Is used to determine the volatility of a stock index.

Answer: C CAPM relates the return on an asset to its beta. The parameter beta measures the sensitivity of the return on the asset to the return on the market. The latter is usually assumed to be the return on a stock index such as the S&P 500.

12. Which of the following best describes “stack and roll”?

A. Creates long-term hedges from short-term futures contracts.

B. Can avoid losses on futures contracts by entering into further futures contracts.

C. Involves buying a futures contract with one maturity and selling a futures contract with a different maturity.

D. Involves two different exposures simultaneously.

Answer: A Stack and roll is a procedure where short maturity futures contracts are entered into. When they are close to maturity, they are replaced by more short maturity futures contracts and so on. The result is the creation of a long-term hedge from short-term futures contracts.

13. Which of the following increases basis risk?

A. A large difference between the futures prices when the hedge is put in place and when it is closed out.

B. Dissimilarity between the underlying asset of the futures contract and the hedger’s exposure.

C. A reduction in the time between the date when the futures contract is closed and its delivery month.

D. None of the above.

Answer: B Basis is the difference between spot and futures at the time the hedge is closed out. This increases as the time between the date when the futures contract is put in place and the delivery month increases. (C is not therefore correct). It also increases as the asset underlying the futures contract becomes more different from the asset being hedged. (B is therefore correct.)

14. Which of the following is a reason for hedging a portfolio with an index futures?

A. The investor believes the stocks in the portfolio will perform better than the market but is uncertain about the future performance of the market.

B. The investor believes the stocks in the portfolio will perform better than the market and the market is expected to do well.

C. The portfolio is not well diversified and so its return is uncertain.

D. All of the above.

Answer: A Index futures can be used to remove the impact of the performance of the overall market on the portfolio. If the market is expected to do well, hedging against the performance of the market is not appropriate. Hedging cannot correct for a poorly diversified portfolio.

15. Which of the following does NOT describe beta?

A. A measure of the sensitivity of the return on an asset to the return on an index.

B. The slope of the best fit line when the return on an asset is regressed against the return on the market.

C. The hedge ratio necessary to remove market risk from a portfolio.

D. Measures correlation between futures prices and spot prices for a commodity.

Answer: D A, B, and C all describe beta but beta has nothing to do with the correlation between futures and spot prices for a commodity.

16. Which of the following is true?

A. Hedging can always be done more easily by a company’s shareholders than by the company itself.

B. If all companies in an industry hedge, a company in the industry can sometimes reduce its risk by choosing not to hedge.

C. If all companies in an industry do not hedge, a company in the industry can reduce its risk by hedging.

D. If all companies in an industry do not hedge, a company is liable to increase its risk by hedging.

Answer: D If all companies in a industry hedge, the price of the end product tends to reflect movements in relevant market variables. Attempting to hedge those movements can therefore increase risk.

17. Which of the following is necessary for tailing a hedge?

A. Comparing the size in units of the position being hedged with the size in units of the futures contract.

B. Comparing the value of the position being hedged with the value of one futures contract.

C. Comparing the futures price of the asset being hedged to its forward price.

D. None of the above.

Answer: B When tailing a hedge, the optimal hedge ratio is applied to the ratio of the value of the position being hedged to the value of one futures contract.

18. Which of the following is true?

A. Gold producers should always hedge the price they will receive for their production of gold over the next three years.

B. Gold producers should always hedge the price they will receive for their production of gold over the next one year.

C. The hedging strategies of a gold producer should depend on whether its shareholders want exposure to the price of gold.

D. Gold producers can hedge by buying gold in the forward market.

Answer: C Some shareholders buy gold stocks to gain exposure to the price of gold. They do not want the company they invest in to hedge. In practice, gold mining companies make their hedging strategies clear to shareholders.

19. A silver mining company has used futures markets to hedge the price it will receive for everything it will produce over the next 5 years. Which of the following is true?

A. It is liable to experience liquidity problems if the price of silver falls dramatically.

B. It is liable to experience liquidity problems if the price of silver rises dramatically.

C. It is liable to experience liquidity problems if the price of silver rises dramatically or falls dramatically.

D. The operation of futures markets protects it from liquidity problems.

Answer: B The mining company shorts futures. It gains on the futures when the price decreases and loses when the price increases. It may get margin calls which lead to liquidity problems when the price rises even though the silver in the ground is worth more.

20. A company will buy 1,000 units of a certain commodity in one year. It decides to hedge 80% of its exposure using futures contracts. The spot price and the futures price are currently $100 and $90, respectively. The spot price and the futures price in one year turn out to be $112 and $110, respectively. What is the average price paid for the commodity?

A. $92 B. $96

C. $102 D. $106 Answer: B On the 80% (hedged) part of the commodity purchase, the price paid will 112 − (110 − 90) or $92. On the other 20%, the price paid will be the spot price of $112. The weighted average of the two prices is 0.8 × 92 + 0.2 × 112 or $96.

Hull: Options, Futures, and Other Derivatives, Eleventh Edition, Global Edition Chapter 4: Interest Rates Multiple Choice Test Bank: Questions with Answers 1. The compounding frequency for an interest rate defines: A. The frequency with which interest is paid.

B. A unit of measurement for the interest rate.

C. The relationship between the annual interest rate and the monthly interest rate.

D. None of the above.

Answer: B The compounding frequency is a unit of measurement. The frequency with which interest is paid may be different from the compounding frequency used for quoting the rate.

2. An interest rate is 6% per annum with annual compounding. What is the equivalent rate with continuous compounding?

A. 5.79% B. 6.21% C. 5.83% D. 6.18% Answer: C The equivalent rate with continuous compounding is ln (1.06) = 0.0583 or 5.83%.

3. An interest rate is 5% per annum with continuous compounding. What is the equivalent rate with semiannual compounding?

A. 5.06% B. 5.03% C. 4.97% D. 4.94% Answer: A The equivalent rate with semiannual compounding is 2 × (e0.05/2 − 1) = 0.0506 or 5.06%.

4. An interest rate is 12% per annum with semiannual compounding. What is the equivalent rate with quarterly compounding?

A. 11.83% B. 11.66% C. 11.77% D. 11.92% Answer: A

The equivalent rate per quarter is 1.06 - 1 = 2.956% . The annualized rate with quarterly compounding is four times this or 11.83%.

5. The two-year zero rate is 6% and the three-year zero rate is 6.5%. What is the forward rate for the third year? All rates are continuously compounded.

A. 6.75% B. 7.0% C. 7.25% D. 7.5% Answer: D The forward rate for the third year is (3 × 0.065 – 2 × 0.06)/(3 − 2) = 0.075 or 7.5%.

6. The six-month zero rate is 8% per annum with semiannual compounding. The price of a oneyear bond that provides a coupon of 6% per annum semiannually is 97. What is the one-year continuously compounded zero rate?

A. 8.02% B. 8.52% C. 9.02% D. 9.52% Answer: C If the rate is R we must have

3 + 103e -R´1 = 97 1.04

or

e -R =

97 - 3 / 1.04 = 0.9137 103

so that R = ln(1/0.9137) = 0.0902 or 9.02%.

7. The yield curve is flat at 6% per annum. What is the value of an FRA where the holder receives interest at the rate of 8% per annum for a six-month period on a principal of $1,000 starting in two years? All rates are compounded semiannually.

A. $9.12 B. $9.02 C. $8.88 D. $8.63 Answer: D The value of the FRA is the value of receiving an extra 0.5 × (0.08 − 0.06) × 1000 = $10 in 2.5 years. This is 10/(1.035) = $8.63.

8. Under liquidity preference theory, which of the following is always true?

A. The forward rate is higher than the spot rate when both have the same maturity.

B. Forward rates are unbiased predictors of expected future spot rates.

C. The spot rate for a certain maturity is higher than the par yield for that maturity.

D. Forward rates are higher than expected future spot rates.

Answer: D Liquidity preference theory argues that individuals like their borrowings to have a long maturity and their deposits to have a short maturity. To induce people to lend for long periods, forward rates are raised relative to what expected future short rates would predict.

9. The zero curve is upward sloping. Define X as the 1-year par yield, Y as the 1-year zero rate and Z as the forward rate for the period between 1 and 1.5 year. Which of the following is true?

A. X is less than Y which is less than Z B. Y is less than X which is less than Z C. X is less than Z which is less than Y D. Z is less than Y which is less than X Answer: A When the zero curve is upward sloping, the one-year zero rate is higher than the one-year par yield and the forward rate corresponding to the period between 1.0 and 1.5 years is higher than the one-year zero rate. The correct answer is therefore A. 10. Which of the following is true of the fed funds rate?

A. It is the same as the Treasury rate.

B. It is an overnight interbank rate.

C. It is a rate for which collateral is posted.

D. It is a type of repo rate.

Answer: B At the end of each day, some banks have surplus reserves on deposit with the Federal Reserve, others have deficits. They use overnight borrowing and lending at what is termed the fed funds rate to rectify this.

11. The modified duration of a bond portfolio worth $1 million is 5 years. By approximately how much does the value of the portfolio change, if all yields increase by 5 basis points?

A. Increase of $2,500 B. Decrease of $2,500 C. Increase of $25,000 D. Decrease of $25,000 Answer: B

When yields increase, bond prices decrease. The proportional decrease is the modified duration times the yield increase. In this case, it is 5 × 0.0005 = 0.0025. The decrease is therefore 0.0025 × 1,000,000 or $2,500.

12. A company invests $1,000 in a five-year zero-coupon bond and $4,000 in a ten-year zero-coupon bond. What is the duration of the portfolio?

A. 6 years B. 7 years C. 8 years D. 9 years Answer: D The duration of the first bond is 5 years and the duration of the second bond is 10 years. The duration of the portfolio is a weighted average with weights corresponding to the amounts invested in the bonds. It is 0.2 × 5 + 0.8 × 10 = 9 years.

13. Which of the following is true of LIBOR? A. The LIBOR rate is free of credit risk.

B. A LIBOR rate is lower than the Treasury rate when the two have the same maturity.

C. It is a rate used when borrowing and lending takes place between banks.

D. It is subject to favorable tax treatment in the U.S. Answer: C LIBOR is a rate used for interbank transactions.

14. Which of following describes forward rates?

A. Interest rates implied by current zero rates for future periods of time.

B. Interest rate earned on an investment that starts today and lasts for n-years in the future without coupons.

C. The coupon rate that causes a bond price to equal its par (or principal) value.

D. A single discount rate that gives the value of a bond equal to its market price when applied to all cash flows.

Answer: A The forward rate is the interest rate implied by the current term structure for future periods of time. For example, earning the zero rate for one year and the forward rate for the period between one and two years gives the same result as earning the zero rate for two years.

15. Which of the following is NOT a theory of the term structure?

A. Expectations theory B. Market segmentation theory C. Liquidity preference theory

D. Maturity preference theory Answer: C Maturity preference theory is not a theory of the term structure. The other three are.

16. What is a repo rate?

A. An uncollateralized rate.

B. A rate where the credit risk is relative high.

C. The rate implicit in a transaction where securities are sold and bought back later at a higher price.

D. None of the above.

Answer: C A repo transaction is one where a company agrees to sell securities today and buy them back at a future time. It is a form of collateralized borrowing. The credit risk is very low.

17. Bootstrapping involves: A. Calculating the yield on a bond.

B. Working from short maturity instruments to longer maturity instruments determining zero rates at each step.

C. Working from long maturity instruments to shorter maturity instruments determining zero rates at each step.

D. The calculation of par yields.

Answer: B Bootstrapping is a way of constructing the zero coupon yield curve from coupon-bearing bonds.

It involves working from the shortest maturity bond to progressively longer maturity bonds making sure that the calculated zero coupon yield curve is consistent with the market prices of the instruments.

18. The zero curve is downward sloping. Define X as the 1-year par yield, Y as the 1-year zero rate and Z as the forward rate for the period between 1 and 1.5 years. Which of the following is true?

A. X is less than Y which is less than Z. B. Y is less than X which is less than Z. C. X is less than Z which is less than Y. D. Z is less than Y which is less than X. Answer: D

The forward rate accentuates trends in the zero curve. The par yield shows the same trends but in a less pronounced way.

19.

Which of the following is true?

A. When interest rates in the economy increase, all bond prices increase.

B. As its coupon increases, a bond’s price decreases.

C. Longer maturity bonds are always worth more that shorter maturity bonds when the coupon rates are the same.

D. None of the above.

Answer: D When interest rates increase, the impact of discounting is to make future cash flows worth less.

Bond prices therefore decline. A is therefore wrong. As coupons increase, a bond becomes more valuable because higher cash flows will be received. B is therefore wrong. When the coupon is higher than prevailing interest rates, longer maturity bonds are worth more than shorter maturity bonds. When it is less than prevailing interest rates, longer maturity bonds are worth less than shorter maturity bonds. C is therefore not true. The correct answer is therefore D.

20.

The six-month and one-year rates are 3% and 4% per annum with semiannual compounding. Which of the following is closest to the one-year par yield expressed with semiannual compounding?

A. 3.99% B. 3.98% C. 3.97% D. 3.96% Answer: A The six-month rate is 1.5% per six months. The one year rate is 2% per six months. The one-year par yield is the coupon that leads to a bond being worth par. A is the correct answer because (3.99/2)/1.015 + (100 + 3.99/2)/1.022 = 100. The formula in the text can also be used to give the par yield as [(100 − 100/1.022) ×2]/(1/1.015 + 1.022) = 3.99.

Hull: Options, Futures, and Other Derivatives, Eleventh Edition, Global Edition Chapter 5: Determination of Forward and Futures Prices Multiple Choice Test Bank: Questions with Answers 1. Which of the following is a consumption asset?

A. The S&P 500 index B. The Canadian dollar C. Copper D. IBM stock Answer: C A, B, and D are investment assets (held by at least some investors purely for investment purposes). C is a consumption asset.

2. An investor shorts 100 shares when the share price is $50 and closes out the position six months later when the share price is $43. The shares pay a dividend of $3 per share during the six months. How much does the investor gain?

A. $1,000 B. $400 C. $700 D. $300 Answer: B The investor gains $7 per share because they sell at $50 and buy at $43. However, the investor has to pay the $3 per share dividend. The net profit is therefore 7 − 3 or $4 per share. 100 shares are involved. The total gain is therefore $400.

3. The spot price of an investment asset that provides no income is $30 and the risk-free rate for all maturities (with continuous compounding) is 10%. What is the three-year forward price?

A. $40.50 B. $22.22 C. $33.00 D. $33.16 Answer: A The 3-year forward price is the spot price grossed up for 3 years at the risk-free rate.

It is 30e0.1×3 = $40.50.

4. The spot price of an investment asset is $30 and the risk-free rate for all maturities is 10% with continuous compounding. The asset provides an income of $2 at the end of the first year and at the end of the second year. What is the three-year forward price?

A. $19.67 B. $35.84 C. $45.15

D. $40.50 Answer: B The present value of the income is 2e-0.1×1 + 2e-0.1×2 = $3.447. The three-year forward price is obtained by subtracting the present value of the income from the current stock price and then grossing up the result for three years at the risk-free rate. It is (30 − 3.447)e0.1×3 = $35.84.

5. An exchange rate is 0.7000 and the six-month domestic and foreign risk-free interest rates are 5% and 7% (both expressed with continuous compounding). What is the six-month forward rate?

A. 0.7070 B. 0.7177 C. 0.7249 D. 0.6930 Answer: D The six-month forward rate is 0.7000e−(0.05−0.07)×0.5 = 0.6930.

6. Which of the following is true?

A. The convenience yield is always positive or zero.

B. The convenience yield is always positive for an investment asset.

C. The convenience yield is always negative for a consumption asset.

D. The convenience yield measures the average return earned by holding futures contracts.

Answer: A The convenience yield measures the benefit of owning an asset rather than having a forward/futures contract on an asset. For an investment asset, it is always zero. For a consumption asset, it is greater than or equal to zero.

7. A short forward contract that was negotiated some time ago will expire in three months and has a delivery price of $40. The current forward price for three-month forward contract is $42. The three-month risk-free interest rate (with continuous compounding) is 8%. What is the value of the short forward contract?

A. +$2.00 B. −$2.00 C. +$1.96 D. −$1.96 Answer: D The contract gives one the obligation to sell for $40 when a forward price negotiated today would give one the obligation to sell for $42. The value of the contract is the present value of −$2 or −2e-0.08×0.25 = −$1.96.

8. The spot price of an asset is positively correlated with the market. Which of the following would you expect to be true?

A. The forward price equals the expected future spot price.

B. The forward price is greater than the expected future spot price.

C. The forward price is less than the expected future spot price.

D. The forward price is sometimes greater and sometimes less than the expected future spot price.

Answer: C When the spot price is positively correlated with the market, the forward price is less than the expected future spot price. This is because the spot price is expected to provide a return greater than the risk-free rate and the forward price is the spot price grossed up at the risk-free rate.

9. Which of the following describes the way the futures price of a foreign currency is quoted by the CME group?

A. The number of U.S. dollars per unit of the foreign currency.

B. The number of the foreign currency per U.S. dollar.

C. Some futures prices are always quoted as the number of U.S. dollars per unit of the foreign currency and some are always quoted the other way round.

D. There are no quotation conventions for futures prices.

Answer: A The futures price is quoted as the number of US dollars per unit of the foreign currency.

Spot exchange rates and forward exchange rates are sometimes quoted this way and sometimes quoted the other way round.

10. Which of the following describes the way the forward price of a foreign currency is quoted?

A. The number of U.S. dollars per unit of the foreign currency.

B. The number of the foreign currency per U.S. dollar.

C. Some forward prices are quoted as the number of U.S. dollars per unit of the foreign currency and some are quoted the other way round.

D. There are no quotation conventions for forward prices.

Answer: C The futures price is quoted as the number of US dollars per unit of the foreign currency.

Spot exchange rates and forward exchange rates are sometimes quoted this way and sometimes quoted the other way round.

11. Which of the following is NOT a reason why a short position in a stock is closed out?

A. The investor with the short position chooses to close out the position.

B. The lender of the shares issues instructions to close out the position.

C. The broker is no longer able to borrow shares from other clients.

D. The investor does not maintain margins required on their margin account.

Answer: B A, C, and D are all reasons why the short position might be closed out. B is not. The lender of shares cannot issue instructions to close out the short position.

12. Which of the following is NOT true?

A. Gold and silver are investment assets.

B. Investment assets are held by significant numbers of investors for investment purposes.

C. Investment assets are never held for consumption.

D. The forward price of an investment asset can be obtained from the spot price, interest rates, and the income paid on the asset.

Answer: C Investment assets are sometimes held for consumption. Silver is an example. To be an investment asset, an asset has to be held for investment by at least some traders.

13. What should a trader do when the one-year forward price of an asset is too low? Assume that the asset provides no income.

A. The trader should borrow the price of the asset, buy one unit of the asset and enter into a short forward contract to sell the asset in one year.

B. The trader should borrow the price of the asset, buy one unit of the asset and enter into a long forward contract to buy the asset in one year.

C. The trader should short the asset, invest the proceeds of the short sale at the risk-free rate, enter into a short forward contract to sell the asset in one year.

D. The trader should short the asset, invest the proceeds of the short sale at the risk-free rate, enter into a long forward contract to buy the asset in one year.

Answer: D If the forward price is too low relative to the spot price, the trader should short the asset in the spot market and buy it in the forward market.

14. Which of the following is NOT true about forward and futures contracts?

A. Forward contracts are more liquid than futures contracts.

B. The futures contracts are traded on exchanges while forward contracts are traded in the over-the-counter market.

C. In theory, forward prices and futures prices are equal when there is no uncertainty about future interest rates.

D. Taxes and transaction costs can lead to forward and futures prices being different.

Answer: A

Futures contracts are more liquid than forward contracts. To unwind a futures position, it is simply necessary to take an offsetting position. The statements in B, C, and D are correct.

15. As the convenience yield increases, which of the following is true?

A. The one-year futures price as a percentage of the spot price increases.

B. The one-year futures price as a percentage of the spot price decreases.

C. The one-year futures price as a percentage of the spot price stays the same.

D. Any of the above can happen.

Answer: B As the convenience yield increases, the futures price declines relative to the spot price. This is because the convenience of owning the asset (as opposed to having a futures contract) becomes more important.

16. As inventories of a commodity decline, which of the following is true?

A. The one-year futures price as a percentage of the spot price increases.

B. The one-year futures price as a percentage of the spot price decreases.

C. The one-year futures price as a percentage of the spot price stays the same.

D. Any of the above can happen.

Answer: B When inventories decline, the convenience yield increases and the futures price as a percentage of the spot price declines.

17. Which of the following describes a known dividend yield on a stock?

A. The size of the dividend payments each year is known.

B. Dividends per year as a percentage of today’s stock price are known.

C. Dividends per year as a percentage of the stock price at the time when dividends are paid are known.

D. Dividends will yield a certain return to a person buying the stock today.

Answer: C The dividend yield is the dividend per year as a percent of the stock price at the time when the dividend is paid.

18. Which of the following is an argument used by Keynes and Hicks?

A. If hedgers hold long positions and speculators hold short positions, the futures price will tend to be higher than the expected future spot price.

B. If hedgers hold long positions and speculators hold short positions, the futures price will tend to be lower than the expected future spot price.

C. If hedgers hold long positions and speculators hold short positions, the futures price will tend to be lower than today’s spot price.

D. If hedgers hold long positions and speculators hold short positions, the futures price will

tend to be higher than today’s spot price.

Answer: A Keynes and Hicks argued that hedgers will be prepared to accept negative returns on average because of the benefits of hedging whereas speculators require positive returns on average.

This leads to A. 19. Which of the following describes contango?

A. The futures price is below the expected future spot price.

B. The futures price is below today’s spot price.

C. The futures price is a declining function of the time to maturity.

D. The futures price is above the expected future spot price.

Answer: D Contango is defined as the futures price being above the expected future spot price. It is also sometimes used to describe the situation where the futures price is above the spot price.

20. Which of the following is true for a consumption commodity?

A. There is no limit to how high or low the futures price can be, except that the futures price cannot be negative.

B. There is a lower limit to the futures price but no upper limit.

C. There is an upper limit to the futures price but no lower limit, except that the futures price cannot be negative.

D. The futures price can be determined with reasonable accuracy from the spot price and interest rates.

Answer: C If the futures price of a consumption commodity becomes too high an arbitrageur will buy the commodity and sell futures to lock in a profit. An arbitrageur cannot follow the opposite strategy of buying futures and selling or shorting the asset when the futures price is low. This is because consumption assets cannot be shorted. Furthermore, people who hold the asset in general do so because they need the asset for their business. They are not prepared to swap their position in the asset for a similar position in a futures. Consequently, there is an upper limit but no lower limit to the futures price.

Hull: Options, Futures, and Other Derivatives, Eleventh Edition, Global Edition Chapter 6: Interest Rate Futures Multiple Choice Test Bank: Questions and Answers 1. Which of following is applicable to corporate bonds in the United States?

A. Actual/360 B. Actual/Actual C. 30/360 D. Actual/365 Answer: C Corporate bonds in the U.S. are usually quoted with a 30/360 day count. This means that there are assumed to be 30 days per month and 360 days per year when the length of an accrual period is calculated.

2.

It is May 1. The quoted price of a bond with an Actual/Actual (in period) day count and 12% per annum coupon (paid semiannually) in the United States is 105. It has a face value of 100 and pays coupons on April 1 and October 1. What is the cash price?

A. 106.00 B. 106.02 C. 105.98 D. 106.04 Answer: C The cash price is the quoted price plus accrued interest. There are 30 actual days between April 1 and May 1 and 183 actual days between April 1 and October 1. In this case the quoted price is 105 and the accrued interest is 0.06 × 100 × 30/183 = 0.98. The answer is therefore 105.98.

3.

It is May 1. The quoted price of a bond with a 30/360 day count and 12% per annum coupon in the United States is 105. It has a face value of 100 and pays coupons on April 1 and October 1.

What is the cash price?

A. 106.00 B. 106.02 C. 105.98 D. 106.04 Answer: A The cash price is the quoted price plus accrued interest. There are 30 assumed days between April 1 and May 1 and 180 assumed days between April 1 and October 1. In this case, the quoted price is 105 and the accrued interest is 0.06 × 100 × 30/180 = 1.00. The answer is therefore 106.00.

4. The most recent settlement bond futures price is 103.5. Which of the following four bonds is the cheapest to deliver?

A. Quoted bond price = 110; conversion factor = 1.0400.

B. Quoted bond price = 160; conversion factor = 1.5200.

C. Quoted bond price = 131; conversion factor = 1.2500.

D. Quoted bond price = 143; conversion factor = 1.3500.

Answer: C The cost of delivering a bond is the quoted bond price minus the most recent settlement price times the conversion factor. This is 2.36, 2.68, 1.625, and 3.275 for bonds in A, B, C, and D, respectively. The bond in C is therefore cheapest to deliver.

5. Which of the following is NOT an option open to the party with a short position in the Treasury bond futures contract?

A. The ability to deliver any of a number of different bonds.

B. The wild card play.

C. The fact that delivery can be made any time during the delivery month.

D. The interest rate used in the calculation of the conversion factor.

Answer: D A, B, and C describe options that the party with the short position has. D does not.

6. A trader enters into a long position in one Eurodollar futures contract. How much does the trader gain when the futures price quote increases by 6 basis points?

A. $6 B. $150 C. $60 D. $600 Answer: B The trader gains $25 for each basis point. The gain is therefore 25 × 6 or $150.

7. The bonds that can be delivered in a Treasury bond futures contract are: A. Assets that provide no income.

B. Assets that provide a known cash income.

C. Assets that provide a known yield.

D. None of the above.

Answer: B A bond is an asset that provides a known cash income (the coupons).

8. An ultra T-bond futures contract is one where: A. Bonds with maturities less than 3 years can be delivered.

B. Bonds with maturities less than 10 years can be delivered.

C. Bonds with maturities greater than 15 years can be delivered.

D. Bonds with maturities greater than 25 year can be delivered.

Answer: D In the ultra T-bond futures contract, bonds with maturities over 25 years can be delivered.

9. A portfolio is worth $24,000,000. The futures price for a Treasury note futures contract is 110 and each contract is for the delivery of bonds with a face value of $100,000. On the delivery date, the duration of the bond that is expected to be cheapest to deliver is 6 years and the duration of the portfolio will be 5.5 years. How many contracts are necessary for hedging the portfolio?

A. 100 B. 200 C. 300 D. 400 Answer: B The contract price is 110,000. The number of contracts is (24,000,000 × 5.5)/(110,000 × 6.0) = 200 10. Which of the following is true?

A. The futures rates calculated from a Eurodollar futures quote are always less than the corresponding forward rate.

B. The futures rates calculated from a Eurodollar futures quote are always greater than the corresponding forward rate.

C. The futures rates calculated from a Eurodollar futures quote should equal the corresponding forward rate.

D. The futures rates calculated from a Eurodollar futures quote are sometimes greater than and sometimes less than the corresponding forward rate.

Answer: B The futures rate must be reduced by what is known as a convexity adjustment to get the forward rate.

11. How much is a basis point?

A. 1.0% B. 0.1% C. 0.01% D. 0.001% Answer: C

A basis point is 0.01%.

12. Which of the following day count conventions applies to a US Treasury bond?

A. Actual/360 B. Actual/Actual (in period) C. 30/360 D. Actual/365 Answer: B Actual/Actual (in period) is used for US Treasury bonds. This means that the interest earned during a period that lies between two coupon payment dates is calculated by dividing the actual number of days in the period by the number of days between the coupon payments and multiplying the result by the next coupon payment.

13. What is the quoted discount rate on a money market instrument?

A. The interest rate earned as a percentage of the final face value of a bond.

B. The interest rate earned as a percentage of the initial price of a bond.

C. The interest rate earned as a percentage of the average price of a bond.

D. The risk-free rate used to calculate the present value of future cash flows from a bond.

Answer: A The quoted discount rate is the interest earned as a percentage of the final face value.

14. Which of the following is closest to the duration of a 2-year bond that pays a coupon of 8% per annum semiannually? The yield on the bond is 10% per annum with continuous compounding.

A. 1.82 B. 1.85 C. 1.88 D. 1.92 Answer: C The duration of the bond is the weighted average of the times when cash flows are received with weights proportional to the present values of the cash flows. This is,

4e -0.10´.5 ´ 0.5 + 4 ´ e -0.10´1 ´1 + 4 ´ e -0.10´1.5 ´1.5 + 104 ´ e -0.10´2 ´ 2 = 1.88 years 4e -0.10´.5 + 4 ´ e -0.10´1 + 4 ´ e -0.10´1.5 + 104 ´ e -0.10´2 15. Which of the following is NOT true about duration?

A. It equals the years-to-maturity for a zero coupon bond.

B. It equals the weighted average of payment times for a bond, where weights are proportional to the present value of payments.

C. Equals the weighted average of individual bond durations for a portfolio, where weights are proportional to the present value of bond prices.

D. The prices of two bonds with the same duration change by the same percentage

amount when interest rate moves up by 100 basis points.

Answer: D D is only approximately true. A, B, and C are exactly true.

16. The conversion factor for a bond is approximately: A. The price it would have if all cash flows were discounted at 6% per annum.

B. The price it would have if it paid coupons at 6% per annum.

C. The price it would have if all cash flows were discounted at 8% per annum.

D. The price it would have if it paid coupons at 8% per annum.

Answer: A The calculation of the conversion factor involves discounting the cash flows on the bond at 6%.

17. The time-to-maturity of a Eurodollar futures contract is 4 years and the time-to-maturity of the rate underlying the futures contract is 4.25 years. The standard deviation of the change in the short-term interest rate, s = 0.011. What does the model in the text estimate as the difference between the futures and the forward interest rate?

A. 0.105% B. 0.103% C. 0.098% D. 0.093% Answer: B With the notation in the text, the futures rate exceeds the forward rate by 0.5s2T1T2. In this case, s = 0.011, T1 = 4 and T2 = 4.25 so the difference between the futures and forward price is 0.5 × 0.011 × 4 × 4.25 = 0.00103.

18. A trader uses 3-month Eurodollar futures to lock in a rate on $5 million for six month s. How many contracts are required?

A. 5 B. 10 C. 15 D. 20 Answer: B Each contract locks in the rate on $1 million dollars for three months. A six-month instrument is approximately twice as sensitive to rate movements as a three- month instrument because it has twice the duration. 2 × 5 = 10 contracts are therefore required.

19. In the U.S., what is the longest maturity for 3-month Eurodollar futures contracts?

A: 2 years B: 5 years

C: 10 years D: 20 years Answer: C Eurodollar futures have maturities out to 10 years.

20. Duration matching immunizes a portfolio against: A. Any parallel shift in the yield curve.

B. All shifts in the yield curve.

C. Changes in the steepness of the yield curve.

D. Small parallel shifts in the yield curve.

Answer: D Duration matching only protects against small parallel shifts. It does not provide protection against large parallel shifts and non-parallel shifts.

Hull: Options, Futures, and Other Derivatives, Eleventh Edition, Global Edition Chapter 7: Swaps Multiple Choice Test Bank: Questions with Answers 1. A company can invest funds for five years at LIBOR minus 30 basis points. The five-year swap rate is 3%. What fixed rate of interest can the company earn by using the swap?

A. 2.4% B. 2.7% C. 3.0% D. 3.3% Answer: B Company earns LIBOR-0.3%. It can pay LIBOR on a swap and receive 3%. This nets to 2.7%.

2. Which of the following is true?

A. Principals are not usually exchanged in a currency swap.

B. The principal amounts usually flow in the opposite direction to interest payments at the beginning of a currency swap and in the same direction as interest payments at the end of the swap.

C. The principal amounts usually flow in the same direction as interest payments at the beginning of a currency swap and in the opposite direction to interest payments at the end of the swap.

D. Principals are not usually specified in a currency swap.

Answer: B The correct answer is B. There are two principals in a currency swap, one for each currency.

They flow in the opposite direction to the corresponding interest payments at the beginning of the life of the swap and in the same direction as the corresponding interest payments at the end of the life of the swap.

3. Which of the following is a way of valuing interest rate swaps where LIBOR is exchanged for a fixed rate of interest?

A. Assume that floating payments will equal forward LIBOR rates and discount net cash flows at the risk-free rate.

B. Assume that floating payments will equal forward OIS rates and discount net cash flows at the risk-free rate.

C. Assume that floating payments will equal forward LIBOR rates and discount net cash flows at the swap rate.

D. Assume that floating payments will equal forward OIS rates and discount net cash flows at the swap rate.

Answer: A Copyright © John Hull 2016. All rights reserved.

A is the correct approach.

4. Which of the following describes the five-year swap rate?

A. The fixed rate of interest which a swap market maker is prepared to pay in exchange for LIBOR on a 5-year swap.

B. The fixed rate of interest which a swap market maker is prepared to receive in exchange for LIBOR on a 5-year swap.

C. The average of A and B. D. The higher of A and B. Answer: C Swap rate is the average of the bid and offers quotes for the swap.

5. Which of the following is a use of a currency swap?

A. To exchange an investment in one currency for an investment in another currency.

B. To exchange borrowing in one currency for borrowings in another currency.

C. To take advantage of situations where the tax rates in two countries are different.

D. All of the above.

Answer: D A currency swap can be used for any of A, B, and C.

6. Which of the following is usually true?

A. OIS rates are less than the corresponding LIBOR rates.

B. OIS rates are greater than corresponding LIBOR rates.

C. OIS rates are sometimes greater and sometimes less than LIBOR rates.

D. OIS rates are equivalent to one-day LIBOR rates.

Answer: A OIS rates are less than the corresponding LIBOR rates. They are “closer to risk-free”.

7. Which of the following describes an interest rate swap?

A. A way of converting a liability from fixed to floating.

B. A portfolio of forward rate agreements.

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C. An agreement to exchange interest at a fixed rate for interest at a floating rate.

D. All of the above.

Answer: D A, B, and C all describe interest rate swaps.

8. Which of the following is true for an interest rate swap?

A. A swap is usually worth close to zero when it is first negotiated.

B. Each forward rate agreement underlying a swap is worth close to zero when the swap is first entered into.

C. Comparative advantage is a valid reason for entering into the swap.

D. None of the above.

Answer: A A swap is worth close to zero at the beginning of its life. (It may not be worth exactly zero because of the impact of the market maker’s bid-offer spread.) It is not true that each of the forward contracts underlying the swap are worth zero. (The sum of the value of the forward contracts is zero, but this does not mean that each one is worth zero.) The remaining floating payments on a swap are worth the notional principal immediately after a swap payment date, but this is not necessarily true for the remaining fixed payments. As explained in the text, the comparative advantage argument is illusory.

9. Which of the following is true for the party paying fixed in an interest rate swap? Assume no other transactions with the counterparty.

A. There is more credit risk when the yield curve is upward sloping than when it is downward sloping.

B. There is more credit risk when the yield curve is downward sloping than when it is upward sloping.

C. The credit exposure increases when interest rates decline.

D. There is no credit exposure provided a financial institution is used as the intermediary.

Answer: A When the yield curve is upward sloping, there is an expectation that the early cash flows will be negative and that the swap will then have a positive value. This increases credit risk.

10. Since the 2008 credit crisis: A. LIBOR has replaced OIS as the discount rate for non-collateralized swaps.

B. OIS has replaced LIBOR as the discount rate, but only for non-collateralized swaps.

C. LIBOR has replaced OIS as the discount rate for collateralized swaps.

D. OIS has replaced LIBOR as the discount rate for swaps.

Answer: D Copyright © John Hull 2016. All rights reserved.

The market has moved from discounting at LIBOR to discounting at OIS. 11. A fixed-for-fixed currency swap: A. Is equivalent to a portfolio of FRAs. B. Is equivalent to a long position in one bond and a short position in another bond.

C. Is worth the same whether or not principals are exchanged.

D. Involves no exchange of principals at the beginning of its life.

Answer: B A fixed-for-fixed currency swap can be regarded as a long position in one bond together with a short position in another. It can also be regarded as a portfolio of forward foreign exchange agreements.

12. A company enters into an interest rate swap where it is paying fixed and receiving LIBOR. When interest rates increase, which of the following is true?

A. The value of the swap to the company increases.

B. The value of the swap to the company decreases.

C. The value of the swap can either increase or decrease.

D. The value of the swap does not change provided the swap rate remains the same.

Answer: A When interest rates increase, the LIBOR rates received are expected to be higher.

13. A floating-for-floating currency swap is equivalent to: A. Two interest rate swaps, one in each currency.

B. A fixed-for-fixed currency swap and one interest rate swap.

C. A fixed-for-fixed currency swap and two interest rate swaps, one in each currency.

D. None of the above.

Answer: C A floating-for-floating currency swap where the currency paid is X and the currency received is Y is equivalent to (a) a fixed-for-fixed currency swap where, say, 5% in currency X is paid and say, say, 4% in currency Y is received, (b) a regular interest rate swap where 5% in currency X is received and floating in currency X is paid, and (c) a regular interest rate swap where 4% in currency Y is paid and floating in currency Y is received.

14. A floating-for-fixed currency swap is equivalent to: A. Two interest rate swaps, one in each currency.

Copyright © John Hull 2016. All rights reserved.

B. A fixed-for-fixed currency swap and one interest rate swap.

C. A fixed-for-fixed currency swap and two interest rate swaps, one in each currency.

D. None of the above.

Answer: B A floating-for-fixed currency swap where the floating rate is paid in currency X and the fixed rate is received in currency Y is equivalent to (a) a fixed-for-fixed currency swap where, say, 5% in currency X is paid and the fixed rate in currency Y is received, and (b) a regular interest rate swap where 5% in currency X is received and floating in currency X is paid.

15. An interest rate swap has three years of remaining life. Payments are exchanged annually.

Interest at 3% is paid and 12-month LIBOR is received. An exchange of payments has just taken place. The one-year, two-year and three-year LIBOR/swap zero rates are 2%, 3% and 4%. All rates are annually compounded. What is the value of the swap as a percentage of the principal when OIS and LIBOR rates are the same?

A. 0.00 B. 2.66 C. 2.06 D. 1.06 Answer: B Suppose the principal 100. The value of the floating rate bond underlying the swap is 100. The value of the fixed rate bond is 3/1.02 + 3/(1.03)2+ 103/(1.04)3= 97.34. The value of the swap is therefore 100 − 97.34 = 2.66 or 2.66% of the principal.

16. A semiannual pay interest rate swap where the fixed rate is 5.00% (with semiannual compounding) has a remaining life of nine months. The six-month LIBOR rate observed three months ago was 4.85% with semiannual compounding. Today’s three- and nine-month LIBOR rates are 5.3% and 5.8% (continuously compounded), respectively. From this, it can be calculated that the forward LIBOR rate for the period between three- and nine-months is 6.14% with semiannual compounding. If the swap has a principal value of $15,000,000, what is the value of the swap to the party receiving a fixed rate of interest? Assume OIS rates are the same as LIBOR rates.

A. $74,250 B. −$70,933 C. −$11,250 D. $103,790 Answer: B

Copyright © John Hull 2016. All rights reserved.

The forward rate for the floating payment at 9 months is 6.05% with continuous compounding or 6.1424% with semiannual compounding. The swap can be valued assuming that the fixed payments are 2.5% of principal at 3 months and 9 months and that the floating payments are 2.425% and 3.0712% of the principal at 3 months and 9 months. The value of the swap to the party receiving fixed is therefore, 15,000,000(0.025-0.02425)e-0.053×0.25+ 15,000,000(0.025-0.030712)e-0.058×0.75 = –$70,933 17. Which of the following describes the way a LIBOR-in-arrears swap differs from a plain vanilla interest rate swap?

A. Interest is paid at the beginning of the accrual period in a LIBOR-in-arrears swap.

B. Interest is paid at the end of the accrual period in a LIBOR-in-arrears swap.

C. No floating interest is paid until the end of the life of the swap in a LIBOR-in-arrears swap, but fixed payments are made throughout the life of the swap.

D. Neither floating nor fixed payments are made until the end of the life of the swap.

Answer: A In a LIBOR-in-arrears swap, interest is observed for an accrual period and paid at the beginning of that accrual period (not at the end of the accrual period which is normal).

18. Which of the following describes a 3-month overnight indexed swap (OIS)?

A. A fixed rate is exchanged for the overnight rate every day for three months.

B. LIBOR is exchanged for the overnight rate every day for three months.

C. The arithmetic average of overnight rates is exchanged for a fixed rate at the end of three months.

D. The geometric average of overnight rates is exchanged for a fixed rate at the end of three months.

Answer: D A three-month OIS is a swap where the geometric average of overnight rates is exchanged for a fixed rate at the end of three months.

19. Which of the following is closest to the bid-offer spread on the swap rate for a plain vanilla interest rate swap?

A. 3 basis points B. 8 basis points C. 13 basis points D. 18 basis points Answer: A 8, 13, and 18 basis points are too high.

Copyright © John Hull 2016. All rights reserved.

20. Which of the following describes the five-year swap rate?

A. The rate on a five-year loan to an AA-rated company.

B. The rate on a five-year loan to an A-rated company.

C. The rate that can be earned over five years from a series of short-term loans to AA-rated companies.

D. The rate that can be earned over five years from a series of short-term loans to A-rated companies.

Answer: C A swap rate is a continually refreshed rate as discussed in the text.

Copyright © John Hull 2016. All rights reserved.

Hull: Options, Futures, and Other Derivatives, Eleventh Edition, Global Edition Chapter 8: Securitization and the Financial Crisis of 2007-8 Multiple Choice Test Bank: Questions with Answers 1. Which of the following tends to lead to an increase in house prices?

A. An increase in interest rates.

B. Regulators specifying a maximum level for the loan-to-value ratio on mortgages.

C. Banks reducing the minimum FICO score that borrowers are required to have.

D. An increase in foreclosures.

Answer: C An increase in interest rates tends to lower house prices because buyers have higher financing costs. Limiting the loan-to-value ratio means that some potential buyers cannot get the mortgages they require and there is less demand for houses with the result that prices tend to decline. An increase in foreclosures increases supply and this also lowers prices. However, if banks relax their lending standards (e.g. by reducing the minimum FICO scores they require), demand should increase because more people can get mortgages. As a result, prices will increase.

2. Which of the following is true of a non-recourse mortgage?

A. The house buyer, if unable to make payments, can lose all his or her possessions.

B. The house buyer has an American-style put option on the house.

C. The house buyer has a European-style put option on the house.

D. The lender is less likely to lose money on the mortgage.

Answer: B In a non-recourse mortgage, a lender cannot seize other assets of the borrower besides the house in order to be repaid. This means that if the price of the house declines below the balance outstanding on the mortgage, the borrower can in principle give the house to the lender in return for tearing up the mortgage. The borrower therefore has an American style put option to sell the house for the amount outstanding on the mortgage.

3. Which of the following is NOT true?

A. The bonus structure at banks can lead to short-term horizons for decision making.

B. Securitization involves the transfer of risk.

C. The term “agency costs” describes the situation where the incentives of two parties in a business relationship are not perfectly aligned.

D. Correlations decrease in stressed market conditions.

Answer: D A, B, and C are true. D is not because correlations tend to increase, not decrease, in stressed markets.

4. Suppose an ABS is created from a portfolio of subprime mortgages with the following allocation of the principal to tranches: senior 80%, mezzanine 10%, and equity 10%. Losses on the mortgage portfolio prove to be 16%. What, as a percent of tranche principal, are losses on the mezzanine tranche of the ABS? A. 50% B. 60% C. 80% D. 100% Answer: B 10% out of the 16% loss is absorbed by the equity tranche. The remaining 6% is absorbed by the mezzanine tranche. The total size of the mezzanine tranche is 10%. It is therefore, 60% wiped out.

5. Suppose that ABSs are created from portfolios of subprime mortgages with the following allocation of the principal to tranches: senior 80%, mezzanine 10%, and equity 10%. (The portfolios of subprime mortgages have the same default rates.) An ABS CDO is then created from the mezzanine tranches of the ABSs with the same allocation of principal. Losses on the mortgage portfolio prove to be 16%. What, as a percent of tranche principal, are losses on the mezzanine tranche of the ABS CDO? A. 50% B. 60% C. 80% D. 100% Answer: D As the answer to the previous question shows, the mezzanine tranches are 60% wiped out. The first 10% out of this 60% is absorbed by the equity tranche of the ABS CDO. The next 10% is absorbed by the mezzanine tranche of the ABS CDO. The remaining 40% is absorbed by the senior tranche of the ABS CDO. The mezzanine tranche of the ABS CDO is therefore 100% wiped out.

6. Suppose that ABSs are created from portfolios of subprime mortgages with the following allocation of the principal to tranches: senior 80%, mezzanine 10%, and equity 10%. (The portfolios of subprime mortgages have the same default rates.) An ABS CDO is then created from the mezzanine tranches with the same allocation of principal. Losses on the mortgage portfolio prove to be 16%. What, as a percent of tranche principal, are losses on the senior tranche of the ABS CDO? A. 50% B. 60% C. 80% D. 100% Answer: A

As the answer to the previous question shows, the senior tranche of the ABS CDO absorbs 40% losses. It is therefore, 40%/80% or 50% wiped out.

7. AIG lost money because: A. It bought tranches created from mortgages.

B. It invested heavily in real estate.

C. It invested heavily in the stock market.

D. It insured AAA tranches of ABS CDOs. Answer: D AIG insured the AAA tranches of ABS CDOs. 8. Which of the following survived the crisis without declaring bankruptcy or being taken over by another financial institution?

A. Bear Stearns B. Morgan Stanley C. Lehman Brothers D. Merrill Lynch Answer: B Morgan Stanley survived. Bear Stearns was taken over by JPMorgan and Merrill Lynch was taken over by Bank of America. Lehman Brothers of course declared bankruptcy.

9. What are teaser rates?

A. Interest rates that appear lower than they are.

B. Interest rates that depend on LIBOR. C. Interest rates on mortgages with a very long amortization period.

D. Interest rates that apply only for the first two or three years.

Answer: D Teaser rates are low interest rates that apply for the first two or three years of a mortgage.

Some house purchasers felt that they could afford mortgage payments based on teaser rates and it was hoped by both the borrower and lender that refinancing would be possible at the end of the teaser rate period.

10. Which of the following describes the waterfall typically used for mortgages pre-crisis?

A. A distribution of cash flows to tranches with priority given to tranche with the highest rating.

B. A distribution of cash flows to tranches in proportion to their outstanding principals.

C. A distribution of losses to tranches so that tranches bear losses in proportion to their outstanding principals.

D. None of the above.

Answer: A The effect of the waterfall was usually that repayments went first to the most senior (highest rated) tranche, then to the next-most-senior tranche, and so on.

11. In 2008, the TED spread reached a high of: A. About 150 basis points.

B. About 250 basis points.

C. About 450 basis points.

D. About 550 basis points.

Answer: C The TED spread is the spread between the three-month LIBOR rate and the three-month Treasury rate. It reached about 450 basis points.

12. Which of the following were introduced before the credit crisis that started in 2007?

A. Basel II B. Dodd-Frank C. Basel III D. Requirements for living wills Answer: A Basel II was first proposed in 1999 and implemented in most parts of the world in about 2007.

The others were introduced after the crisis had started.

13. Which of the following is true as the correlation between mortgage defaults increases?

A. Equity tranches are almost certain to incur losses.

B. Senior tranches become more likely to incur losses.

C. The expected number of defaults increases.

D. Equity tranches are unaffected.

Answer: B If the correlation between mortgage defaults is very low the senior tranche is safe, but as the correlation increases it becomes more likely that it will experience losses. Suppose that the default probability is 2%. When correlation is zero, we expect roughly 2% of mortgages to default each year and there is virtually no chance of the senior tranche bearing losses. In the limit when default correlation between mortgages is perfect, the senior tranche has a 2% chance of bearing losses in any given year.

14. Which of the following describes the S&P/Case-Shiller index?

A. A stock market index.

B. An index of interest rates on mortgages.

C. An index of house prices.

D. An index showing the dollar amount of mortgages granted each month.

Answer: C The S&P/Case-Shiller index is an index of house prices.

15. Suppose that ABSs are created from portfolios of subprime mortgages with the following allocation of the principal to tranches: senior 85%, mezzanine 10%, and equity 5%. (The portfolios of subprime mortgages have the same default rates.) An ABS CDO is then created from the mezzanine tranches with the same allocation of principal. How high can losses on the mortgages be before the mezzanine tranche of the ABD CDO bears losses?

A. 5.0% B. 5.5% C. 6.0% D. 6.5% Answer: B If losses are 5.5%, the mezzanine tranches of ABSs lose 0.5/10 or 5% of their principal. The mezzanine tranche of the ABS CDO is then safe (just).

16. Suppose that ABSs are created from portfolios of subprime mortgages with the following allocation of the principal to tranches: senior 85%, mezzanine 10%, and equity 5%. (The portfolios of subprime mortgages have the same default rates.) An ABS CDO is then created from the mezzanine tranches with the same allocation of principal. How high can losses on the mortgages be before the senior tranche of the ABS CDO bears losses?

A. 5.5% B. 6.0% C. 6.5% D. 7.0% Answer: C If losses are 6.5%, the mezzanine tranches of ABSs lose 1.5/10 or 15% of their principal. The senior tranches of the ABS CDO is then safe (just).

17. Suppose that ABSs are created from portfolios of subprime mortgages with the following allocation of the principal to tranches: senior 94.5% (rated AAA), mezzanine 0.1% (rated BBB), and equity 5% (rated C). The portfolios of subprime mortgages have the same default rates. An ABS CDO is then created from the mezzanine tranches. Which of the following is true?

A. The ABS CDO tranches should have ratings ranging from AAA to C. B. The ABS CDO tranches should all be rated BBB. C. The ABS CDO tranches should all be rated C. D. The ABS CDO tranches are almost worthless because the mezzanine tranches are so thin.

Answer: B Because they are so thin, the mezzanine tranches of the ABS are either all safe or all wiped out.

The tranches created from them are therefore essentially the same.

18. Which of the following describes regulatory arbitrage?

A. Finding a way of reducing capital requirements without changing the risks being taken.

B. Buying products that are not subject to regulation.

C. Shorting products that are not subject to regulation.

D. Trading with the government.

Answer: A Regulatory arbitrage involves organizing trading and accounting so that regulatory capital is reduced without the risks being taken changing.

19. Which of the following describes a subprime mortgage?

A. The rate of interest is less than the prime rate of interest.

B. The loan-to-value ratio is below average.

C. The life of the mortgage is less than 25 years.

D. The credit risk is high.

Answer: D There is no precise definition of a subprime mortgage. But one thing we can be sure of is that it has more credit risk than a normal mortgage.

20. Which of the following would be described by the term “liar loan”?

A. A situation where the lender concealed information from the borrower.

B. A situation where the lender lied to the borrower about the interest rate.

C. A situation where the borrower lied about income.

D. None of the above.

Answer: C A liar loan is a loan where the borrower lied in some way on the application form.

Hull: Options, Futures, and Other Derivatives, Eleventh Edition, Global Edition Chapter 9: XVAs Multiple Choice Test Bank: Questions with Answers 1. Which of the following is NOT a valuation adjustment?

A. CVA B. MVA C. ZVA D. KVA Answer: C CVA is credit valuation adjustments; MVA is margin valuation adjustment; KVA is capital valuation adjustment. ZVA is not a valuation adjustment.

2. What does CVA stands for?

A. Collateral valuation adjustment B. Credit valuation adjustment C. Credit valuation agreement D. Collateral valuation agreement Answer: B CVA stands for credit value adjustment.

3. What does DVA stands for?

A. Debt valuation adjustment B. Debt valuation agreement C. Debt variation adjustment D. Debit valuation agreement Answer: A DVA stands for debt (or debit) valuation adjustment.

4. When a bank’s borrowing rate goes up, which of the following is true?

A. DVA increases so that the bank’s profit goes down.

B. DVA increases so that the bank’s profit goes up.

C. DVA declines so that the bank’s profit goes down.

D. DVA declines so that the bank’s profit goes up.

Answer: B

The bank is considered more likely to default and its DVA therefore increases. This increases its profit because it is then considered more likely that it will default and not have to meet derivatives obligations.

5. Which of the following is true?

A. CVA and DVA can be calculated deal by deal.

B. CVA and DVA must both be calculated for the whole portfolio a bank has with a counterparty.

C. CVA can be calculated deal by deal but DVA must be calculated for a portfolio.

D. DVA can be calculated deal by deal but CVA must be calculated for a portfolio.

Answer: B Because of netting, all derivatives in a portfolio are considered to be a single derivative in the event of a default. CVA which measures the cost of a counterparty default and DVA which measures the benefit of the bank defaulting must therefore be calculated on a portfolio basis.

6. It is assumed that a company can default after one year or after two years. The probability of default at each time is 1.5%. The present value of the expected loss to a bank on a derivatives portfolio if the company defaults after one year is estimated to be $1 million. The present value of the expected loss if it defaults after two years is estimated to be $2 million. Which of the following is the bank’s CVA? A. $3,000,000 B. $300,000 C. $45,000 D. $150,000 Answer: C The present value of the expected loss is 0.015 × $1,000,000 + 0.015 × $2,000,000 or $45,000.

This is the CVA. 7. A bank has three uncollateralized transactions with a counterparty worth +$10 million, −$20 million and +$25 million. A netting agreement is in place. What is the maximum loss if the counterparty defaults today?

A. $15 million B. $35 million C. $20 million D. Zero Answer: A The netting agreement means that the three transactions are considered to be a single transaction. The net value of the transactions to the bank is 10 – 20 + 25 or $15 million. This is the maximum amount that could be lost if the counterparty defaults today.

8. Which of the following involves most credit risk?

A. Exchange trading B. OTC trading with a central clearing party being used.

C. OTC trading with bilateral clearing and collateral being posted.

D. OTC trading with bilateral clearing and no collateral being posted.

Answer: D In the case of both exchange trading and trading using a CCP, initial margin and variation margin have to be posted so that the risk of a loss because of a default is low. Bilateral clearing usually involves more credit risk than exchange/CCP trading and credit risk is greater when there is no collateral agreement.

9. FVA is concerned with: A. The cost of funding initial margin.

B. The cost of funding variation margin.

C. The cost of regulatory capital.

D. None of the above.

Answer: B FVA is concerned with the cost of funding variation margin.

10. MVA is concerned with: A. The cost of funding initial margin.

B. The cost of funding variation margin.

C. The cost of regulatory capital.

D. None of the above.

Answer: A MVA is concerned with the cost of funding initial margin.

11. KVA is concerned with: A. The cost of funding initial margin.

B. The cost of funding variation margin.

C. The cost of regulatory capital.

D. None of the above.

Answer: C KVA is concerned with the cost of regulatory capital.

12. CVA is concerned with: A. The cost of funding initial margin.

B. The cost of funding variation margin.

C. The cost of regulatory capital.

D. None of the above.

Answer: D CVA is concerned with the cost of a counterparty default.

13. Financial economics argues that: A. All investments by a company should earn the company’s weighted average cost of capital.

B. The required expected return on an investment is the average cost of debt.

C. The required expected return on an investment increases with the riskiness of the investment.

D. The required expected return on an investment decreases with the riskiness of the investment.

Answer: C The return required on an investment should in theory reflect its risk not how it is financed.

14. Financial economics argues that as the percentage of equity in the capital structure increases: A. The required return on both equity and debt decrease.

B. The required return on equity decreases and the required return on debt increases.

C. The required return on equity increases and the required return on debt decreases.

D. The required return on both equity and debt increase.

Answer: A As equity increases, both the debt and equity become less risky to the investor.

15. DVA for a bank is most dependent on: A. The default probabilities of the bank in future time periods.

B. The default probabilities of the bank’s counterparties in future times periods.

C. Both A and B. D. Neither A nor B. Answer: A DVA is the cost to the counterparty (benefit to the bank) arising from the possibility of a default by the bank. It is the bank’s default probabilities that are relevant.

16. Which of the following is true?

A. FVA is always positive.

B. FVA is always negative.

C. FVA for a transaction is initially zero.

D. None of the above.

Answer: D FVA can be positive or negative. For example, the incremental FVA from the uncollateralized sale of an option is negative whereas that from the purchase of an option is positive.

17. Prior to the credit crisis that started in 2007, which of the following was used by derivatives traders for the discount rate when derivatives were valued?

A. The Treasury rate B. The LIBOR rate C. The repo rate D. The overnight indexed swap rate Answer: B Derivatives markets used LIBOR as the discount rate pre-crisis.

18. Since the credit crisis that started in 2007, which of the following have derivatives traders used as the risk-free discount rate for collateralized transactions?

A. The Treasury rate B. The LIBOR rate C. The repo rate D. The overnight indexed swap rate Answer: D Derivatives markets have used the OIS rate as the discount rate for collateralized transactions since the crisis.

19. Which of the following is true?

A. OIS rates are less than the corresponding LIBOR/swap rates.

B. OIS rates are greater than corresponding LIBOR/swap rates.

C. OIS rates are sometimes greater and sometimes less than LIBOR/swap rates.

D. OIS rates are equivalent to one-day LIBOR rates.

Answer: A OIS rates are less than LIBOR /swap rates when both have the same maturity.

20. Which of the following is approximately true?

A. FVA can be calculated from the initial value of a derivative.

B. FVA can be calculated on a transaction-by-transaction basis without considering the whole portfolio of derivatives a dealer has with a counterparty.

C. FVA should theoretically depend on a dealer’s funding cost.

D. None of the above.

Answer: B The (positive or negative) funding arising from variation margin is additive across transactions.

Hull: Options, Futures, and Other Derivatives, Eleventh Edition, Global Edition Chapter 10: Mechanics of Options Markets Multiple Choice Test Bank: Questions with Answers 1. Which of the following describes a call option?

A. The right to buy an asset for a certain price.

B. The obligation to buy an asset for a certain price.

C. The right to sell an asset for a certain price.

D. The obligation to sell an asset for a certain price.

Answer: A A call option is the right, but not the obligation to buy.

2. Which of the following is true?

A. A long call is the same as a short put.

B. A short call is the same as a long put.

C. A call on a stock plus a stock is the same as a put.

D. None of the above.

Answer: D None of the statements are true. Long calls, short calls, long puts, and short puts all have different payoffs as indicated by Figure 10.5. A put on a stock plus the stock provides a payoff that is similar to a call, as explained in Chapters 11 and 12. But a call on a stock plus a stock does not provide a similar payoff to a put.

3. An investor has exchange-traded put options to sell 100 shares for $20. There is a 2 for 1 stock split. Which of the following is the position of the investor after the stock split?

A. Put options to sell 100 shares for $20.

B. Put options to sell 100 shares for $10.

C. Put options to sell 200 shares for $10.

D. Put options to sell 200 shares for $20.

Answer: C When there is a stock split, the number of shares increases and the strike price decreases. In this case, because it is a 2 for 1 stock split, the number of shares doubles and the strike price halves.

4. An investor has exchange-traded put options to sell 100 shares for $20. There is 25% stock dividend. Which of the following is the position of the investor after the stock dividend?

A. Put options to sell 100 shares for $20.

B. Put options to sell 75 shares for $25.

C. Put options to sell 125 shares for $15.

D. Put options to sell 125 shares for $16.

Answer: D The stock dividend is equivalent to a 5 for 4 stock split. The number of shares goes up by 25% and the strike price is reduced to 4/5 of its previous value.

5. An investor has exchange-traded put options to sell 100 shares for $20. There is a $1 cash dividend. Which of the following is then the position of the investor?

A. The investor has put options to sell 100 shares for $20.

B. The investor has put options to sell 100 shares for $19.

C. The investor has put options to sell 105 shares for $19.

D. The investor has put options to sell 105 shares for $19.05.

Answer: A Cash dividends unless they are unusually large have no effect on the terms of an option.

6. Which of the following describes a short position in an option?

A. A position in an option lasting less than one month.

B. A position in an option lasting less than three months.

C. A position in an option lasting less than six months.

D. A position where an option has been sold.

Answer: D A short position is a position where the option has been sold (the opposite to a long position).

7. Which of the following describes a difference between a warrant and an exchange-traded stock option?

A. In a warrant issue, someone has guaranteed the performance of the option seller in the event that the option is exercised.

B. The number of warrants is fixed whereas the number of exchange-traded options in existence depends on trading.

C. Exchange-traded stock options have a strike price.

D. Warrants cannot be traded after they have been purchased.

Answer: B A warrant is a fixed number of options issued by a company. They often trade on an exchange after they have been issued.

8. Which of the following describes LEAPS? A. Options which are partly American and partly European.

B. Options where the strike price changes through time.

C. Exchange-traded stock options with longer lives than regular exchange-traded stock options.

D. Options on the average stock price during a period of time.

Answer: C LEAPS are long-term equity anticipation securities. They are exchange-traded options with relatively long maturities.

9. Which of the following is an example of an option class?

A. All calls on a certain stock.

B. All calls with a particular strike price on a certain stock.

C. All calls with a particular time to maturity on a certain stock.

D. All calls with a particular time to maturity and strike price on a certain stock.

Answer: A An option class is all calls on a certain stock or all puts on a certain stock.

10. Which of the following is an example of an option series?

A. All calls on a certain stock.

B. All calls with a particular strike price on a certain stock.

C. All calls with a particular time to maturity on a certain stock.

D. All calls with a particular time to maturity and strike price on a certain stock.

Answer: D All options on a certain stock of a certain type (calls or put) with a certain strike price and time to maturity are referred to as an option series.

11. Which of the following must post margin?

A. The seller of an option.

B. The buyer of an option.

C. The seller and the buyer of an option.

D. Neither the seller nor the buyer of an option.

Answer: A The seller of the option must post margin as a guarantee that the payoff on the option (if there is one) will be made. The buyer of the option usually pays for the option upfront and so no margin is required.

12. Which of the following describes a long position in an option?

A. A position where there is more than one year to maturity.

B. A position where there is more than five years to maturity.

C. A position where an option has been purchased.

D. A position that has been held for a long time.

Answer: C A long position is a position where an option has been purchased. It can be contrasted with a short position which is a position where an option has been sold.

13. Which of the following is NOT traded by the CBOE? A. Weeklys B. Monthlys C. Binary options D. DOOM options Answer: B Monthlys are not a CBOE product. The others are.

14. When a six-month option is purchased: A. The price must be paid in full.

B. Up to 25% of the option price can be borrowed using a margin account.

C. Up to 50% of the option price can be borrowed using a margin account.

D. Up to 75% of the option price can be borrowed using a margin account.

Answer: A Only options lasting more than 9 months can be bought on margin.

15. Which of the following are true for CBOE stock options?

A. There are no margin requirements.

B. The initial margin and maintenance margin are determined by formulas and are equal.

C. The initial margin and maintenance margin are determined by formulas and are different.

D. The maintenance margin is usually about 75% of the initial margin.

Answer: B Margin accounts for options must be brought up to the initial/maintenance margin level every day.

16. The price of a stock is $67. A trader sells 5 put option contracts on the stock with a strike price of $70 when the option price is $4. The options are exercised when the stock price is $69. What is the trader’s net profit or loss?

A. Loss of $1,500 B. Loss of $500 C. Gain of $1,500 D. Loss of $1,000 Answer: C The option payoff is 70 − 69 = $1. The amount received for the option is $4. The gain is $3 per option. In total 5 × 100 = 500 options are sold. The total gain is therefore $3 × 500 = $1,500.

17. A trader buys a call and sells a put with the same strike price and maturity date. What is the position equivalent to?

A. A long forward B. A short forward C. Buying the asset D. None of the above Answer: A From adding up the two payoffs, we see that A is true: max(ST −K,0) −max(K − ST,0) = ST−K 18. The price of a stock is $64. A trader buys 1 put option contract on the stock with a strike price of $60 when the option price is $10. When does the trader make a profit?

A. When the stock price is below $60.

B. When the stock price is below $64.

C. When the stock price is below $54.

D. When the stock price is below $50.

Answer: D The payoff must be more than the $10 paid for the option. The stock price must therefore be below $50.

19. Consider a put option and a call option with the same strike price and time to maturity. Which of the following is true?

A. It is possible for both options to be in the money.

B. It is possible for both options to be out of the money.

C. One of the options must be in the money.

D. One of the options must be either in the money or at the money.

Answer: D If the stock price is greater than the strike price, the call is in the money and the put is out of the money. If the stock price is less than the strike price, the call is out of the money and the put is in the money. If the stock price is equal to the strike price, both options are at the money.

20. In which of the following cases is an asset NOT considered constructively sold?

A. The owner shorts the asset.

B. The owner buys an in-the-money put option on the asset.

C. The owner shorts a forward contract on the asset.

D. The owner shorts a futures contract on the stock.

Answer: B Profits on the asset have to be recognized in A, C, and D. The holder of the asset cannot defer recognition of profits with the trades indicated. In the case of B, the asset is not considered constructively sold. Buying a deep-in-the-money put option is a way of almost certainly locking in a profit on an asset without triggering an immediate tax liability.

Hull: Options, Futures, and Other Derivatives, Eleventh Edition, Global Edition Chapter 11: Properties of Stock Options Multiple Choice Test Bank: Questions with Answers 1. When the stock price increases with all else remaining the same, which of the following is true?

A. Both calls and puts increase in value.

B. Both calls and puts decrease in value.

C. Calls increase in value while puts decrease in value.

D. Puts increase in value while calls decrease in value.

Answer: C Stock price increases cause the values of calls to increase and the values of puts to decline.

2. When the strike price increases with all else remaining the same, which of the following is true?

A. Both calls and puts increase in value.

B. Both calls and puts decrease in value.

C. Calls increase in value while puts decrease in value.

D. Puts increase in value while calls decrease in value.

Answer: D Strike price increases cause the values of puts to increase and the values of calls to decline.

3. When volatility increases with all else remaining the same, which of the following is true?

A. Both calls and puts increase in value.

B. Both calls and puts decrease in value.

C. Calls increase in value while puts decrease in value.

D. Puts increase in value while calls decrease in value.

Answer: A Volatility increases the likelihood of a high payoff from either a call or a put option. The payoff can never be negative. It follows that as volatility increases the value of all options increase.

4. When dividends increase with all else remaining the same, which of the following is true?

A. Both calls and puts increase in value.

B. Both calls and puts decrease in value.

C. Calls increase in value while puts decrease in value.

D. Puts increase in value while calls decrease in value.

Answer: D Dividends during the life of an option reduce the final stock price. As a result dividend increases cause puts to increase in value and calls to decrease in value.

5. When interest rates increase with all else remaining the same, which of the following is true?

A. Both calls and puts increase in value.

B. Both calls and puts decrease in value.

C. Calls increase in value while puts decrease in value.

D. Puts increase in value while calls decrease in value.

Answer: C Calls increase and puts decrease in value. As explained in the text, an increase in interest rates causes the growth rate of the stock price to increase and the discount rate to increase.

An increase in interest rates therefore reduces the value of puts because puts are hurt by both a discount rate increase and a growth rate increase. For calls, it turns out that the growth rate increase is more important than the discount rate increase so that their values increase when interest rates increase. (Note that we are assuming all else equal and so the asset price does not change.)

6. When the time to maturity increases with all else remaining the same, which of the following is true?

A. European options always increase in value.

B. The value of European options either stays the same or increases.

C. There is no effect on European option values.

D. European options are liable to increase or decrease in value.

Answer: D When the time to maturity increases from X to Y, European options usually increase in value. But this is not always the case. For example, European call options can decrease in value if a big dividend is expected between X and Y. 7. The price of a stock, which pays no dividends, is $30 and the strike price of a one year European call option on the stock is $25. The risk-free rate is 4% (continuously compounded). Which of the following is a lower bound for the option such that there are arbitrage opportunities if the price is below the lower bound and no arbitrage opportunities if it is above the lower bound?

A. $5.00 B. $5.98 C. $4.98 D. $3.98 Answer: B The lower bound in S0 − Ke-rT. In this case it is 30 – 25e-0.04×1 = $5.98.

8. A stock price (which pays no dividends) is $50 and the strike price of a two year European put option is $54. The risk-free rate is 3% (continuously compounded). Which of the following is a lower bound for the option such that there are arbitrage opportunities if the price is below the

lower bound and no arbitrage opportunities if it is above the lower bound?

A. $4.00 B. $3.86 C. $2.86 D. $0.86 Answer: D The lower bound in Ke-rT −S0. In this case, it is 54e−0.03×2 – 50 = $0.86.

9. Which of the following is NOT true? (Present values are calculated from the end of the life of the option to the beginning.)

A. An American put option is always worth less than the present value of the strike price.

B. A European put option is always worth less than the present value of the strike price.

C. A European call option is always worth less than the stock price.

D. An American call option is always worth less than the stock price.

Answer: A If it is optimal to exercise an American option today and the stock price is very low, the option will be worth more than the present value of the strike price.

10. Which of the following best describes the intrinsic value of an option?

A. The value it would have if the owner had to exercise it immediately or not at all.

B. The Black-Scholes-Merton price of the option.

C. The lower bound for the option’s price.

D. The amount paid for the option.

Answer: A The intrinsic value of an option is the value it would have if it were about to expire which is the same as the value in A. 11. Which of the following describes a situation where an American put option on a stock becomes more likely to be exercised early?

A. Expected dividends increase B. Interest rates decrease C. The stock price volatility decreases D. All of the above Answer: C As the volatility of the option decreases, the time value declines and the option becomes

more likely to be exercised early. In the case of A and B, time value increases and the option is less likely to be exercised early.

12. Which of the following is true?

A. An American call option on a stock should never be exercised early.

B. An American call option on a stock should never be exercised early when no dividends are expected.

C. There is always some chance that an American call option on a stock will be exercised early.

D. There is always some chance that an American call option on a stock will be exercised early when no dividends are expected.

Answer: B An American call option should never be exercised early when the underlying stock does not pay dividends. There are two reasons. First, it is best to delay paying the strike price.

Second, the insurance provided by the option (that the stock price will fall below the strike price) is lost.

13. Which of the following is the put-call parity result for a non-dividend-paying stock?

A. The European put price plus the European call price must equal the stock price plus the present value of the strike price.

B. The European put price plus the present value of the strike price must equal the European call price plus the stock price.

C. The European put price plus the stock price must equal the European call price plus the strike price.

D. The European put price plus the stock price must equal the European call price plus the present value of the strike price.

Answer: D The put-call parity result is c + Ke-rT= p + S0.

14. Which of the following is true when dividends are expected?

A. Put-call parity does not hold.

B. The basic put-call parity formula can be adjusted by subtracting the present value of expected dividends from the stock price.

C. The basic put-call parity formula can be adjusted by adding the present value of expected dividends to the stock price.

D. The basic put-call parity formula can be adjusted by subtracting the dividend yield from the interest rate.

Answer: B Put call parity still holds for European options providing the present value of the dividends is subtracted from the stock price.

15. The price of a European call option on a non-dividend-paying stock with a strike price of $50 is $6. The stock price is $51, the continuously compounded risk-free rate (all maturities) is 6% and the time to maturity is one year. What is the price of a one-year European put option on the stock with a strike price of $50?

A. $9.91 B. $7.00 C. $6.00 D. $2.09 Answer: D Put-call parity is c+Ke-rT=p+S0. In this case K = 50, S0 = 51, r = 0.06, T = 1, and c = 6. It follows that p = 6 + 50e-0.06×1 − 51 = 2.09.

16. The price of a European call option on a stock with a strike price of $50 is $6. The stock price is $51, the continuously compounded risk-free rate (all maturities) is 6% and the time to maturity is one year. A dividend of $1 is expected in six months. What is the price of a one-year European put option on the stock with a strike price of $50?

A. $8.97 B. $6.97 C. $3.06 D. $1.12 Answer: C Put-call parity is c + Ke-rT = p + S0˗D. In this case K = 50, S0 = 51, r = 0.06, T = 1, and c = 6.

The present value of the dividend, D, is 1 × e−0.06×0.5 = 0.97. It follows that p = 6 + 50e-0.06×1− (51− 0.97) = 3.06.

17. A European call and a European put on a stock have the same strike price and time to maturity.

At 10:00 am on a certain day, the price of the call is $3 and the price of the put is $4. At 10:01 am news reaches the market that has no effect on the stock price or interest rates, but increases volatilities. As a result, the price of the call changes to $4.50. Which of the following is correct?

A. The put price increases to $6.00.

B. The put price decreases to $2.00.

C. The put price increases to $5.50.

D. It is possible that there is no effect on the put price.

Answer: C

The price of the call has increased by $1.50. From put-call parity the price of the put must increase by the same amount. Hence, the put price will become 4.00 + 1.50 = $5.50.

18. Interest rates are zero. A European call with a strike price of $50 and a maturity of one year is worth $6. A European put with a strike price of $50 and a maturity of one year is worth $7. The current stock price is $49. Which of the following is true?

A. The call price is high relative to the put price.

B. The put price is high relative to the call price.

C. Both the call and put must be mispriced.

D. None of the above.

Answer: D In this case because interest rates are zero c + K = p + S0. The left side of this equation is 50 + 6 = 56. The right side is 49 + 7 = 56. There is no mispricing.

19. Which of the following is true for American options?

A. Put-call parity provides an upper and a lower bound for the difference between call and put prices.

B. Put call parity provides an upper bound but no lower bound for the difference between call and put prices.

C. Put call parity provides a lower bound but no upper bound for the difference between call and put prices.

D. There are no put-call parity results.

Answer: A Put call parity provides both an upper and a lower bound for the difference between call and put prices. See equation (11.11).

20. Which of the following can be used to create a long position in a European put option on a stock?

A. Buy a call option on the stock and buy the stock.

B. Buy a call on the stock and short the stock.

C. Sell a call option on the stock and buy the stock.

D. Sell a call option on the stock and sell the stock.

Answer: B As payoff diagrams show, a call on a stock combined with a short position in the stock gives a payoff similar to a put option. Alternatively, we can use put-call parity, which shows that a call minus the stock equals the put minus the present value of the strike price.

Hull: Options, Futures, and Other Derivatives, Eleventh Edition, Global Edition Chapter 12: Trading Strategies Involving Options Multiple Choice Test Bank: Questions with Answers 1. Which of the following creates a bull spread?

A. Buy a low strike price call and sell a high strike price call.

B. Buy a high strike price call and sell a low strike price call.

C. Buy a low strike price call and sell a high strike price put.

D. Buy a low strike price put and sell a high strike price call.

Answer: A A bull spread is created by buying a low strike call and selling a high strike call. Alternatively, it can be created by buying a low strike put and selling a high strike put.

2. Which of the following creates a bear spread?

A. Buy a low strike price call and sell a high strike price call.

B. Buy a high strike price call and sell a low strike price call.

C. Buy a low strike price call and sell a high strike price put.

D. Buy a low strike price put and sell a high strike price call.

Answer: B A bear spread is created by buying a high strike call and selling a low strike call.

Alternatively, it can be created by buying a high strike put and selling a low strike put.

3. Which of the following creates a bull spread?

A. Buy a low strike price put and sell a high strike price put.

B. Buy a high strike price put and sell a low strike price put.

C. Buy a high strike price call and sell a low strike price put.

D. Buy a high strike price put and sell a low strike price call.

Answer: A A bull spread is created by buying a low strike call and selling a high strike call. Alternatively, it can be created by buying a low strike put and selling a high strike put.

4.

Which of the following creates a bear spread?

A. Buy a low strike price put and sell a high strike price put.

B. Buy a high strike price put and sell a low strike price put.

C. Buy a high strike price call and sell a low strike price put.

D. Buy a high strike price put and sell a low strike price call.

Answer: B

A bear spread is created by buying a high strike call and selling a low strike call.

Alternatively, it can be created by buying a high strike put and selling a low strike put.

5. What is the number of different option series used in creating a butterfly spread?

A. 1 B. 2 C. 3 D. 4 Answer: C Three different options all with the same maturity are involved in creating a butterfly spread. The strike prices are usually equally spaced. The creator buys the low strike option, buys the high strike option, and sells two of the intermediate strike option.

6. A stock price is currently $23. A reverse (i.e., short) butterfly spread is created from options with strike prices of $20, $25, and $30. Which of the following is true?

A. The gain when the stock price is greater than $30 is less than the gain when the stock price is less than $20.

B. The gain when the stock price is greater than $30 is greater than the gain when the stock price is less than $20.

C. The gain when the stock price is greater than $30 is the same as the gain when the stock price is less than $20.

D. It is incorrect to assume that there is always a gain when the stock price is greater than $30 or less than $20.

Answer: C The gain from a very high stock price or a very low stock price is the same. Suppose calls are used. In the case of a very low stock price, none are exercised and the gain is c1 + c3 − 2c2 from the option premium. In the case of a very high stock price, all options are exercised.

The net payoff is zero and the gain is the same.

7. Which of the following is correct?

A. A calendar spread can be created by buying a call and selling a put when the strike prices are the same and the times to maturity are different.

B. A calendar spread can be created by buying a put and selling a call when the strike prices are the same and the times to maturity are different.

C. A calendar spread can be created by buying a call and selling a call when the strike prices are different and the times to maturity are different.

D. A calendar spread can be created by buying a call and selling a call when the strike prices are the same and the times to maturity are different.

Answer: D A calendar spread is created by buying an option with one maturity and selling an option with another maturity when the strike prices are the same and the option types (calls or puts) are the same.

8. What is a description of the trading strategy where an investor sells a 3-month call option and buys a one-year call option, where both options have a strike price of $100 and the underlying stock price is $75?

A. Neutral Calendar Spread B. Bullish Calendar Spread C. Bearish Calendar Spread D. None of the above Answer: B This is a bullish calendar spread because a big increase in the stock price between three months and one year is necessary for the trading strategy to be profitable.

9. Which of the following is correct?

A. A diagonal spread can be created by buying a call and selling a put when the strike prices are the same and the times to maturity are different.

B. A diagonal spread can be created by buying a put and selling a call when the strike prices are the same and the times to maturity are different.

C. A diagonal spread can be created by buying a call and selling a call when the strike prices are different and the times to maturity are different.

D. A diagonal spread can be created by buying a call and selling a call when the strike prices are the same and the times to maturity are different.

Answer: C Both the strike prices and times to maturity are different in a diagonal spread.

10. Which of the following is true of a box spread?

A. It is a package consisting of a bull spread and a bear spread.

B. It involves two call options and two put options.

C. It has a known value at maturity.

D. All of the above.

Answer: D

A, B, and C are all true.

11. How can a straddle be created?

A. Buy one call and one put with the same strike price and same expiration date.

B. Buy one call and one put with different strike prices and same expiration date.

C. Buy one call and two puts with the same strike price and expiration date.

D. Buy two calls and one put with the same strike price and expiration date.

Answer: A A straddle consists of one call and one put where the strike price and time to maturity are the same. It has a V-shaped payoff.

12. How can a strip trading strategy be created?

A. Buy one call and one put with the same strike price and same expiration date.

B. Buy one call and one put with different strike prices and same expiration date.

C. Buy one call and two puts with the same strike price and expiration date.

D. Buy two calls and one put with the same strike price and expiration date.

Answer: C A strip consists of one call and two puts with the same strike price and time to maturity.

13. How can a strap trading strategy be created?

A. Buy one call and one put with the same strike price and same expiration date.

B. Buy one call and one put with different strike prices and same expiration date.

C. Buy one call and two puts with the same strike price and expiration date.

D. Buy two calls and one put with the same strike price and expiration date.

Answer: D A strap consists of two calls and one put with the same strike price and time to maturity.

14. How can a strangle trading strategy be created?

A. Buy one call and one put with the same strike price and same expiration date.

B. Buy one call and one put with different strike prices and same expiration date.

C. Buy one call and two puts with the same strike price and expiration date.

D. Buy two calls and one put with the same strike price and expiration date.

Answer: B A strangle can be created with one call and one put where the times to maturity are the same but the call strike price is greater than the put strike price.

15. Which of the following describes a protective put?

A. A long put option on a stock plus a long position in the stock.

B. A long put option on a stock plus a short position in the stock.

C. A short put option on a stock plus a short call option on the stock.

D. A short put option on a stock plus a long position in the stock.

Answer: A A protective put consists of a long put plus the stock. The holder of the put owns the stock that might become deliverable.

16. Which of the following describes a covered call?

A. A long call option on a stock plus a long position in the stock.

B. A long call option on a stock plus a short put option on the stock.

C. A short call option on a stock plus a short position in the stock.

D. A short call option on a stock plus a long position in the stock.

Answer: D A covered call consists of a short call plus a long position in the stock. Then the owner of the position has the stock ready to deliver if the other side exercises the call.

17. When the interest rate is 5% per annum with continuous compounding, which of the following creates a principal protected note worth $1000?

A. A one-year zero-coupon bond plus a one-year call option worth about $59.

B. A one-year zero-coupon bond plus a one-year call option worth about $49.

C. A one-year zero-coupon bond plus a one-year call option worth about $39.

D. A one-year zero-coupon bond plus a one-year call option worth about $29.

Answer: B A one-year zero-coupon bond is worth 1000e-0.05×1 or about $951. This leaves 1000 − 951 = $49 for buying the option.

18. A trader creates a long butterfly spread from options with strike prices $60, $65, and $70 by trading a total of 400 options. The options are worth $11, $14, and $18. What is the maximum net gain (after the cost of the options is taken into account)?

A. $100 B. $200 C. $300 D. $400 Answer: D The butterfly spread involves buying 100 options with strike prices $60 and $70 and selling 200 options with strike price $65. The maximum gain is when the stock price equals the middle strike price, $65. The payoffs from the options are then, $500, 0, and 0, respectively.

The total payoff is $500. The cost of setting up the butterfly spread is 11 × 100 + 18 × 100 – 14 × 200 = $100. The gain is 500 − 100 or $400.

19. A trader creates a long butterfly spread from options with strike prices $60, $65, and $70 by trading a total of 400 options. The options are worth $11, $14, and $18. What is the maximum net loss (after the cost of the options is taken into account)?

A. $100 B. $200 C. $300 D. $400 Answer: A The butterfly spread involves buying 100 options with strike prices $60 and $70 and selling 200 options with strike price $65. The maximum loss is when the stock price is less than $60 or greater than $70. The total payoff is then zero. The cost of setting up the butterfly spread is 11 × 100 + 18 × 100 – 14 × 200 = $100. The loss is therefore $100.

20. Six-month call options with strike prices of $35 and $40 cost $6 and $4, respectively. What is the maximum gain when a bull spread is created by trading a total of 200 options?

A. $100 B. $200 C. $300 D. $400 Answer: C The bull spread involves buying 100 calls with strike $35 and selling 100 calls with strike price $40. The cost is 6 × 100 – 4 × 100 = $200. The maximum payoff (when the stock price is greater than or equal to $40) is $500. The maximum gain is therefore 500 − 200 = $300.

Hull: Options, Futures, and Other Derivatives, Eleventh Edition, Global Edition Chapter 13: Binomial Trees Multiple Choice Test Bank: Questions with Answers 1. The current price of a non-dividend-paying stock is $30. Over the next six months it is expected to rise to $36 or fall to $26. Assume the risk-free rate is zero. An investor sells six-month call options with a strike price of $32. Which of the following hedges the position?

A. Buy 0.6 shares for each call option sold.

B. Buy 0.4 shares for each call option sold.

C. Short 0.6 shares for each call option sold.

D. Short 0.4 shares for each call option sold.

Answer: B The value of the option will be either $4 or zero. If D is the position in the stock, we require 36D − 4 = 26D so that D = 0.4. It follows that 0.4 shares should be purchased for each option sold.

2. The current price of a non-dividend-paying stock is $30. Over the next six months, it is expected to rise to $36 or fall to $26. Assume the risk-free rate is zero. What is the risk-neutral probability of that the stock price will be $36?

A. 0.6 B. 0.5 C. 0.4 D. 0.3 Answer: C The formula for the risk-neutral probability of an up movement is

e rT - d p= u-d

In this case u = 36/30 or 1.2 and d = 26/30 = 0.8667. Also r = 0 and T = 0.5. The formula gives p = (1 − 0.8667/(1.2 − 0.8667) = 0.4.

3. The current price of a non-dividend-paying stock is $30. Over the next six months, it is expected to rise to $36 or fall to $26. Assume the risk-free rate is zero. An investor sells call options with a strike price of $32. What is the value of each call option?

A. $1.6 B. $2.0 C. $2.4 D. $3.0 Answer: A The formula for the risk-neutral probability of an up movement is

p=

e rT - d u-d

In this case u = 36/30 or 1.2 and d = 26/30 = 0.8667. Also r = 0 and T = 0.5. The formula gives p = (1 − 0.8667/(1.2 − 0.8667) = 0.4.

The payoff from the call option is $4 if there is an up movement and $0 if there is a down movement. The value of the option is therefore 0.4 × 4 + 0.6 × 0 = $1.6. (We do not do any discounting because the interest rate is zero.)

4. The current price of a non-dividend-paying stock is $40. Over the next year, it is expected to rise to $42 or fall to $37. An investor buys one-year put options with a strike price of $41. Which of the following is necessary to hedge the position?

A. Buy 0.2 shares for each option purchased.

B. Sell 0.2 shares for each option purchased.

C. Buy 0.8 shares for each option purchased.

D. Sell 0.8 shares for each option purchased.

Answer: C The payoff from the put option is zero if there is an up movement and 4 if there is a down movement. Suppose that the investor buys one put option and buys D shares. If there is an up movement, the value of the portfolio is D × 42. If there is a down movement, it is worth D × 37 + 4. These are equal when 37D + 4 = 42D or D = 0.8. The investor should therefore buy 0.8 shares for each option purchased.

5. The current price of a non-dividend-paying stock is $40. Over the next year, it is expected to rise to $42 or fall to $37. An investor buys put options with a strike price of $41. What is the value of each option? The risk-free interest rate is 2% per annum with continuous compounding.

A. $3.93 B. $2.93 C. $1.93 D. $0.93 Answer: D The formula for the risk-neutral probability of an up movement is

e rT - d p= u-d In this case, r = 0.02, T = 1, u = 42/40 = 1.05 and d = 37/40 = 0.925 so that p = 0.76 and the value of the option is (0.76 × 0 + 0.24 × 4)e-0.02×1 = 0.93

6. Which of the following describes how American options can be valued using a binomial tree?

A. Check whether early exercise is optimal at all nodes where the option is in-the-money.

B. Check whether early exercise is optimal at the final nodes.

C. Check whether early exercise is optimal at the penultimate nodes and the final nodes.

D. None of the above.

Answer: A For an American option, we must check whether exercising is better than not exercising at each node where the option is in the money. (It is clearly not worth exercising when the option is out of the money) 7. In a binomial tree created to value an option on a stock, the expected return on stock is: A. Zero B. The return required by the market C. The risk-free rate D. It is impossible to know without more information.

Answer: C The expected return on the stock on the tree is the risk-free rate. This is an application of risk-neutral valuation.

8. In a binomial tree created to value an option on a stock, what is the expected return on the option?

A. Zero B. The return required by the market C. The risk-free rate D. It is impossible to know without more information.

Answer: C The expected return on the option on the tree is the risk-free rate. This is an application of risk-neutral valuation. The expected return on all assets in a risk-neutral world is the riskfree rate.

9. A stock is expected to return 10% when the risk-free rate is 4%. What is the correct discount rate to use for the expected payoff on an option in the real world?

A. 4% B. 10% C. More than 10% D. It could be more or less than 10%.

Answer: D The correct answer is D. There is no easy way of determining the correct discount rate for an option’s expected payoff in the real world. For a call option, the correct discount rate in the real world is often quite high and for a put option it is often quite low (even negative). The

example in the text illustrates this.

10. Which of the following is true for a call option on a stock worth $50?

A. As a stock’s expected return increases, the price of the option increases.

B. As a stock’s expected return increases, the price of the option decreases.

C. As a stock’s expected return increases, the price of the option might increase or decrease.

D. As a stock’s expected return increases, the price of the option on the stock stays the same.

Answer: D The option price when expressed in terms of the underlying stock price is independent of the return on the stock. To put this another way, everything relevant about the expected return is incorporated in the stock price.

11. Which of the following are NOT true?

A. Risk-neutral valuation and no-arbitrage arguments give the same option prices.

B. Risk-neutral valuation involves assuming that the expected return is the risk-free rate and then discounting expected payoffs at the risk-free rate.

C. A hedge set up to value an option does not need to be changed.

D. All of the above.

Answer: C The hedge set up to value an option needs to be changed as time passes. A and B are true.

12. The current price of a non-dividend paying stock is $30. Use a two-step tree to value a European call option on the stock with a strike price of $32 that expires in 6 months. Each step is 3 months, the risk free rate is 8% per annum with continuous compounding. What is the option price when u = 1.1 and d = 0.9?

A. $1.29 B. $1.49 C. $1.69 D. $1.89 Answer: B The probability of an up movement is

p= The tree is

e rDt - d e 0.08´0.25 - 0.9 = = 0.6010 u-d 1.1 - 0.9

36.3 4.3 33 2.533 30 1.492

29.7 0 27 0 24.3 0

13. The current price of a non-dividend paying stock is $30. Use a two-step tree to value a European put option on the stock with a strike price of $32 that expires in 6 months with u = 1.1 and d = 0.9. Each step is 3 months, the risk free rate is 8%.

A. $2.24 B. $2.44 C. $2.64 D. $2.84 Answer: A The probability of an up movement is

p= The tree is

e rDt - d e 0.08´0.25 - 0.9 = = 0.6010 u-d 1.1 - 0.9 36.3 0

33 0.9 30 2.238

29.7 2.3 27 4.366 24.3 7.7

14. Which of the following is NOT true in a risk-neutral world?

A. The expected return on a call option is independent of its strike price.

B. Investors expect higher returns to compensate for higher risk.

C. The expected return on a stock is the risk-free rate.

D. The discount rate used for the expected payoff on an option is the risk-free rate.

Answer: B In a risk-neutral world, investors require an expected return equal to the risk-free rate and the discount rate that should be used for all expected payoffs is the risk-free rate.

15. If the volatility of a non-dividend paying stock is 20% per annum and a risk-free rate is 5% per annum, which of the following is closest to the Cox, Ross, Rubinstein parameter u for a tree with a three-month time step?

A. 1.05 B. 1.07 C. 1.09 D. 1.11 Answer: D The formula for u is

u = e s Dt = e 0.2´ 0.25 = 1.1052 16. If the volatility of a non-dividend-paying stock is 20% per annum and a risk-free rate is 5% per annum, which of the following is closest to the Cox, Ross, Rubinstein parameter p for a tree with a three-month time step?

A. 0.50 B. 0.54 C. 0.58 D. 0.62 Answer: B The formula for p is

p=

e rDt - d e 0.05´0.25 - 0.9048 =0.538 = u-d 1.1052 - 0.9048

17. The current price of a non-dividend paying stock is $50. Use a two-step tree to value an American put option on the stock with a strike price of $48 that expires in 12 months. Each step is 6

months, the risk free rate is 5% per annum, and the volatility is 20%. Which of the following is the option price?

A. $1.95 B. $2.00 C. $2.05 D. $2.10 Answer: B In this case

u = e s Dt = e 0.2´ 0.5 = 1.152 p=

d = 1 / u = 0.868

e rDt - d e 0.05´0.5 - 0.868 = = 0.5539 u-d 1.152 - 0.868

The tree is

66.34482 0 57.5955 0 50 1.999

50 0 43.40617 4.593828 37.68192 10.31808

18. Which of the following describes delta?

A. The ratio of the option price to the stock price.

B. The ratio of the stock price to the option price.

C. The ratio of a change in the option price to the corresponding change in the stock price.

D. The ratio of a change in the stock price to the corresponding change in the option price.

Answer: C Delta is Df/DS where DS is a small change in the stock price (with nothing else changing) and Df is the corresponding change in the option price.

19. When moving from valuing an option on a non-dividend paying stock to an option on a currency, which of the following is true?

A. The risk-free rate is replaced by the excess of the domestic risk-free rate over the foreign risk-free rate in all calculations.

B. The formula for u changes.

C. The risk-free rate is replaced by the excess of the domestic risk-free rate over the foreign risk-free rate for discounting.

D. The risk-free rate is replaced by the excess of the domestic risk-free rate over the foreign risk-free rate when p is calculated.

Answer: D The formula for u does not change. The discount rate does not change. The formula for p becomes

p= showing that D is correct.

e

( r - r f ) Dt

-d u-d

20. A tree is constructed to value an option on an index which is currently worth 100 and has a volatility of 25%. The index provides a dividend yield of 2%. Another tree is constructed to value an option on a non-dividend-paying stock which is currently worth 100 and has a volatility of 25%. Which of the following are true?

A. The parameters p and u are the same for both trees.

B. The parameter p is the same for both trees but u is not.

C. The parameter u is the same for both trees but p is not.

D. None of the above.

Answer: C

The formula for u is the same in the two cases so that the values of the index on its tree are the same as the values of the stock on its tree. However, in the formula for p, r is replaced by r − q.

Hull: Options, Futures, and Other Derivatives, Eleventh Edition, Global Edition Chapter 14: Wiener Processes and Ito’s Lemma Multiple Choice Test Bank: Questions with Answers 1. A variable x starts at 10 and follows the generalized Wiener process dx = a dt + b dz where time is measured in years. If a = 2 and b = 3, what is the expected value after 3 years?

A. 12 B. 14 C. 16 D. 18 Answer: C The drift is 2 per year and so the expected increase over three years is 2 × 3 = 6 and the expected value at the end of 3 years is 10 + 6 = 16.

2. A variable x starts at 10 and follows the generalized Wiener process dx = a dt + b dz where time is measured in years. If a = 3 and b = 4, what is the standard deviation of the value in 4 years?

A. 4 B. 8 C. 12 D. 16 Answer: B The variance per year is 42 or 16. The variance over four years is 16 × 4 = 64. The standard deviation is 64 = 8 .

3. A variable x starts at 10 and follows the generalized Wiener process dx = a dt + b dz If a = 3 and b = 4, what is the standard deviation of the value in three months?

A. 1 B. 2 C. 3 D. 4 Answer: B The variance per year is 42 or 16. The variance over three months is 16 × 0.25 = 4. The standard deviation is 4 = 2 .

4. The variance of a Wiener process in time t is: A. t B. t squared C. the square root of t D. t to the power of 4 Answer: A The variance of a Wiener process is 1 per unit time or t in time t.

5. The process followed by a variable X is dX = mX dt + sX dz What is the coefficient of dz in the process for the square of X. A. sX B. sX2 C. 2sX2 D. msX Answer: C From Ito’s lemma, the coefficient of dz is sX ¶f ¶X where f = X2. Because ¶f ¶X = 2 X , the coefficient of dz is 2sX2.

6. The process followed by a variable X is dX = mX dt+sX dz What is the coefficient of dt in the process for the square of X. A. 2mX2+ s2X2 B. 2mX2 C. mX2 + 2s2X2 D. mX2 + s2X2 Answer: A From Ito’s lemma, the coefficient of dt is

¶f 1 2 2 ¶ 2 f + s X ¶X 2 ¶X 2 where f = X2. Because ¶f ¶X = 2 X and ¶ 2 f ¶X 2 = 2 the coefficient of dt is 2mX2 + s2X2 mX

7. Which of the following is true when the stock price follows the geometric Brownian motion?

A. The future stock price has a normal distribution.

B. The future stock price has a lognormal distribution.

C. The future stock price has a geometric distribution.

D. The future stock price has a truncated normal distribution.

Answer: B Ito’s lemma show that the log of the stock price follows a generalized Wiener process. This means that the log of the stock price is normally distributed so that the stock price is lognormally distributed.

8. If a stock price follows a Markov process, which of the following could be true?

A. Whenever the stock price has gone up for four successive days, it has a 70% chance of going up on the fifth day.

B. Whenever the stock price has gone up for four successive days, there is almost certain to be a correction on the fifth day.

C. The way the stock price moves on a day is unaffected by how it moved on the previous four days.

D. Bad years for stock price returns are usually followed by good years.

Answer: C A Markov process is a particular type of stochastic process where only the current value of a variable is relevant for predicting the future. Stock prices are usually assumed to follow Markov processes. This corresponds to a weak form market efficiency assumption.

9. A variable x starts at zero and follows the generalized Wiener process dx = a dt + b dz where time is measured in years. During the first two years a = 3 and b = 4. During the following three years, a = 6 and b = 3. What is the expected value of the variable at the end of 5 years?

A. 16 B. 20 C. 24 D. 30 Answer: C During the first two years, the drift per year is 3 and so the total drift is 3 × 2 or 6. During the next three years, the drift per year is 6 and the total drift is 6 × 3 = 18. The total drift over the five years is 6 + 18 = 24. Given that the variable starts at zero, its expected value at the end of the five years is therefore 24.

10. A variable x starts at zero and follows the generalized Wiener process dx = a dt + b dz

where time is measured in years. During the first two years, a = 3 and b = 4. During the following three years, a = 6 and b = 3. What the standard deviation of the value of the variable at the end of 5 years?

A. 6.2 B. 6.7 C. 7.2 D. 7.7 Answer: D The variance per year for the first two years is 42 or 16. The variance per year for the next three years is 32 or 9. The total variance of the change over five years is 2 × 16 + 3 × 9 = 59. The standard deviation of the value of the variable at the end of the five years is therefore

59 = 7.7 .

11. If a variable x follows the process dx = b dz where dz is a Wiener process, which of the following is the process followed by y = exp(x)?

A. dy = by dz B. dy = 0.5b2y dt + by dz C. dy = (y + 0.5b2y) dt + by dz D. dy = 0.5b2y dt + b dz Answer: B Ito’s lemma shows that the process followed by y is dy = 0.5b2exp(x) dt + bexp(x) dz. Substituting y = exp(x), we get the answer in B. 12. If the risk-free rate is r and price of a nondividend paying stock grows at rate m with volatility s, at what rate does a forward price of the stock grow for a forward contract maturing at a future time T? A. m B. m − s2/2 C. m − r D. r − s2/2 Answer: C This is the application of Ito’s lemma in Section 14.6.

13. When a stock price, S, follows geometric Brownian motion with mean return m and volatility s what is the process follows by X where X = ln S? A. dX = m dt + s dz B. dX = (m −r) dt + s dz C. dX = (m −s2) dt + s dz D. dX = (m − s2/2) dt + s dz Answer: D This is the example in Section 14.7 14. Which of the following gives a random sample from a standard normal distribution in Excel?

A. =NORMSINV() B. =NORMSINV(RAND()) C. =RND(NORMSINV()) D. =RAND() Answer: B The correct instruction in Excel is =NORMSINV(RAND()) 15. Which of the following defines an Ito process?

A. A process where the drift is non-constant and can be stochastic.

B. A process where the coefficient of dz is non-constant and can be stochastic.

C. A process where either the drift or the coefficient of dz or both are non-constant and can be stochastic.

D. A process where proportional changes follow a generalized Wiener process.

Answer: C In a generalized Wiener process, the drift and coefficient of dz are both constant. In an Ito process, they are not both constant.

16. A stock price is $20. It has an expected return of 12% and a volatility of 25%. What is the standard deviation of the change in the price in one day? (For this question assume that there are 365 days in the year.)

A. $0.20

B. $0.23 C. $0.26 D. $0.29 Answer: C The standard deviation of the change in one day is 20 ´ 0.25 ´ 1/ 365 = $0.26 .

17. A stock price is $20. It has an expected return of 12% and a volatility of 25%. What is the stock price that has a 2.5% chance of being exceeded in one day? (For this question, assume that there are 365 days in the year.)

A. $20.41 B. $20.51 C. $20.61 D. $20.71 Answer: B From the previous question the standard deviation of the change in one day is $0.26. There is a 2.5% chance that the stock price will increase by more than 1.96 standard deviations. The answer is therefore 20 + 1.96 × 0.26 = $20.51. The expected return in one day is small and can be ignored.

18. Which of the following is NOT a property of a Wiener process?

A. The change during a short period of time dt has a variance dt.

B. The changes in two different short periods of time are independent.

C. The mean change in any time period is zero.

D. The standard deviation over two consecutive time periods is the sum of the standard deviations over each of the periods.

Answer: D Variances of Wiener processes are additive but standard deviations are not.

19. If e is a random sample from a standard normal distribution, which of the following is the change in a Wiener process in time dt?

A. e times the square root of dt B. e times dt C. dt times the square root of e D. The square root of e times the square root of dt Answer: A

The change is e dt . This result is used when the process is simulated.

20. For what value of the correlation between two Wiener processes is the sum of the processes also a Wiener process?

A. 0.5 B. −0.5 C. 0 D. 1 Answer: B The variance of each process is 1 per unit time. The variance of the sum is 1 + 1 + 2r where r is the correlation. This is 1 when r = −0.5.

Hull: Options, Futures, and Other Derivatives, Eleventh Edition, Global Edition Chapter 15: The Black–Scholes–Merton Model Multiple Choice Test Bank: Questions with Answers 1. Which of the following is assumed by the Black–Scholes–Merton model?

A. The return from the stock in a short period of time is lognormal.

B. The stock price at a future time is lognormal.

C. The stock price at a future time is normal.

D. None of the above.

Answer: B Black–Scholes–Merton assumes that the return from a stock in a short period of time is normally distributed. This means that the stock price at a future time is lognormally distributed.

2. The original Black–Scholes and Merton papers on stock option pricing were published in which year?

A. 1983 B. 1984 C. 1974 D. 1973 Answer: D The correct answer is 1973. By coincidence, this is also the year that organized trading in call options started. Put option trading started a few years later.

3. Which of the following is a definition of volatility?

A. The standard deviation of the return, measured with continuous compounding, in one year.

B. The variance of the return, measured with continuous compounding, in one year.

C. The standard deviation of the stock price in one year.

D. The variance of the stock price in one year.

Answer: A Volatility when multiplied by the square root of Dt is the standard deviation of the return in a short period of time of length Dt. It is also the standard deviation of the continuously compounded return in one year.

4. A stock price is $100. Volatility is estimated to be 20% per year. What is an estimate of the standard deviation of the change in the stock price in one week?

A. $0.38 B. $2.77

C. $3.02 D. $0.76 Answer: B The estimate is 100 ´ 0.2 ´ 1 / 52 = $2.77 .

5. What does N(x) denote?

A. The area under a normal distribution from zero to x.

B. The area under a normal distribution up to x.

C. The area under a normal distribution beyond x.

D. The area under the normal distribution between -x and x.

Answer: B The normal distribution runs from minus infinity to plus infinity. N(x) is the area under the distribution between minus infinity and x.

6. Which of the following is true for a one-year call option on a stock that pays dividends every three months?

A. It is never optimal to exercise the option early.

B. It can be optimal to exercise the option at any time.

C. It is only ever optimal to exercise the option immediately after an ex-dividend date.

D. None of the above.

Answer: D When there are dividends, it is sometimes optimal to exercise immediately before an exdividend date, but it is never optimal to exercise at other times. None of the first three answers are therefore correct.

7. What is the number of trading days in a year usually assumed for equities?

A. 365 B. 252 C. 262 D. 272 Answer: B Analysts usually assume that there are 252 trading days in a year for equities.

8. The risk-free rate is 5% and the expected return on a non-dividend-paying stock is 12%. Which of the following is a way of valuing a derivative?

A. Assume that the expected growth rate for the stock price is 17% and discount the expected payoff at 12%.

B. Assuming that the expected growth rate for the stock price is 5% and discounting the

expected payoff at 12%.

C. Assuming that the expected growth rate for the stock price is 5% and discounting the expected payoff at 5%.

D. Assuming that the expected growth rate for the stock price is 12% and discounting the expected payoff at 5%.

Answer: C Risk-neutral valuation shows that a derivative can be correctly valued by assuming that the stock grows at the risk-free rate and discounting the expected payoff at the risk-free rate. It follows that C is the correct answer.

9. When there are two dividends on a stock, Black’s approximation sets the value of an American call option equal to which of the following?

A. The value of a European option maturing just before the first dividend.

B. The value of a European option maturing just before the second (final) dividend.

C. The greater of the values in A and B. D. The greater of the value in B and the value assuming no early exercise.

Answer: D For Black’s approximation we calculate: a) the value of the option assuming no early exercise, and b) the value of the option assuming that the exercise decision is made immediately before the final ex-dividend date. The value of the option is set equal to the greater of these two values.

10. Which of the following is measured by the VIX index?

A. Implied volatilities for stock options trading on the CBOE. B. Historical volatilities for stock options trading on CBOE. C. Implied volatilities for options trading on the S&P 500 index.

D. Historical volatilities for options trading on the S&P 500 index.

Answer: C The VIX index measures the implied volatilities of one-month options trading on the S&P 500 index.

11. What was the original Black–Scholes–Merton model designed to value?

A. A European option on a stock providing no dividends.

B. A European or American option on a stock providing no dividends.

C. A European option on any stock.

D. A European or American option on any stock.

Answer: A The original Black–Scholes–Merton model was designed to value a European option on a stock paying no dividends.

12. A stock provides an expected return of 10% per year and has a volatility of 20% per year. What is the expected value of the continuously compounded return in one year?

A. 6% B. 8% C. 10% D. 12% Answer: B The expected value of the continuously compounded return per year is µ - s / 2. In this case, it is 0.1 – 0.22/2 = 0.08 or 8%.

2

13. An investor has earned 2%, 12% and –10% on equity investments in successive years (annually compounded). This is equivalent to earning which of the following annually compounded rates for the three year period.

A. 1.33% B. 1.23% C. 1.13% D. 0.93% Answer: D Over the three year period, $100 grows to 100 × 1.02 × 1.12 × 0.9 = $102.816. This corresponds to an annually compounded return per year of 3 1.02816 - 1 = 0.0093 or 0.93%. One plus the return is the geometric average of 1.02, 1.12, and 0.90.

14. Which of the following is NOT true?

A. Risk-neutral valuation provides prices that are only correct in a world where investors are risk-neutral.

B. Options can be valued based on the assumption that investors are risk neutral.

C. In risk-neutral valuation, the expected return on all investment assets is set equal to the risk-free rate.

D. In risk-neutral valuation, the risk-free rate is used to discount expected cash flows.

Answer: A Risk-neutral valuation produces a valuation that is correct in all situations not just those where investors are risk-neutral. The expected return on all investments is assumed to be the risk-free rate and the risk-free rate is used to discount expected payoffs.

15. Which of the following is a way of extending the Black–Scholes–Merton formula to value a European call option on a stock paying a single dividend?

A. Reduce the maturity of the option so that it equals the time of the dividend.

B. Subtract the dividend from the stock price.

C. Add the dividend to the stock price.

D. Subtract the present value of the dividend from the stock price.

Answer: D To value a European option, we replace the stock price by the stock price minus the present value of all dividends that have ex-dividend dates during the life of the option.

16. When the Black–Scholes–Merton and binomial tree models are used to value an option on a non-dividend-paying stock, which of the following is true?

A. The binomial tree price converges to a price slightly above the Black–Scholes–Merton price as the number of time steps is increased.

B. The binomial tree price converges to a price slightly below the Black–Scholes–Merton price as the number of time steps is increased.

C. Either A or B can be true.

D. The binomial tree price converges to the Black–Scholes–Merton price as the number of time steps is increased.

Answer: D The binomial tree valuation method and the Black–Scholes–Merton formula are based on the same set of assumptions. As the number of time steps is increased, the answer given by the binomial tree approach converges to the answer given by the Black–Scholes–Merton formula.

17. When the non-dividend paying stock price is $20, the strike price is $20, the risk-free rate is 6%, the volatility is 20% and the time to maturity is 3 months which of the following is the price of a European call option on the stock?

A. 20N(0.1) –19.7N(0.2) B. 20N(0.2) –19.7N(0.1) C. 19.7N(0.2) –20N(0.1) D. 19.7N(0.1) –20N(0.2) Answer: B The formula for the option price is

S 0 N (d 1 ) - Ke - rT N (d 2 ) d1 =

ln(S 0 / K ) + (r + s 2 / 2)T s T

and

d 2 = d1 - s T

In this case, S0 = K = 20, r = 0.06, s = 0.2, and T = 0.25 so that Ke-rT = 20e-0.06×0.25 = 19.7. Also d1 = [ln(1) + (0.06 + 0.04/2) × 0.25]/(0.2 × 0.5) = 0.2 and d2 = 0.2 – 0.2 × 0.5 = 0.1.

B is therefore the correct answer.

18. When the non-dividend paying stock price is $20, the strike price is $20, the risk-free rate is 6%, the volatility is 20% and the time to maturity is 3 months, which of the following is the price of a European put option on the stock?

A. 19.7N(–0.1) –20N(–0.2) B. 20N(–0.1) –20N(–0.2) C. 19.7N(–0.2) –20N(–0.1) D. 20N(–0.2) –20N(–0.1)

Answer: A The formula for the option price is

Ke - rT N (-d 2 ) - S 0 N (-d 1 ) d1 =

ln(S 0 / K ) + (r + s 2 / 2)T s T

and

d 2 = d1 - s T

In this case, S0 = K = 20, r = 0.06, s = 0.2, and T = 0.25 so that Ke-rT = 20e-0.06×0.25= 19.7. Also d1 = [ln(1) + (0.06 + 0.04/2) × 0.25]/(0.2 × 0.5) = 0.2 and d2 = 0.2 – 0.2 × 0.5 = 0.1.

A is therefore the correct answer.

19. A stock price is 20, 22, 19, 21, 24, and 24 on six successive Fridays. Which of the following is closest to the volatility per annum estimated from this data?

A. 50% B. 60% C. 70% D. 80% Answer: D The price relative for the first week is 22/20 or 1.1. The natural log of the price relative is ln(1.1) or 0.09531. Similarly, the ln of the price relatives for the other weeks are –0.1466, 0.1001, 0.1335, and 0. The standard deviation of 0.09531, –0.1466, 0.1001, 0.1335, and 0 is 0.1138. The volatility per week is therefore 11.38%. This corresponds to a volatility per year of 0.1138 multiplied by the square root of 52 or about 82%. The answer is therefore D. 20. The volatility of a stock is 18% per year. Which is closest to the volatility per month?

A. 1.5% B. 3.0% C. 5.2% D. 6.3% Answer: C The volatility per month is the volatility per year multiplied by the square root of 1/12. The square root of 1/12 is 0.2887 and 18% multiplied by this is 5.2%.

Hull: Options, Futures, and Other Derivatives, Eleventh Edition, Global Edition Chapter 16: Employee Stock Options Multiple Choice Test Bank: Questions with Answers 1. Which of the following is true?

A. An employee stock option is usually held to maturity.

B. An employee stock option tends to be exercised earlier than a traded option with the same terms.

C. An employee stock options tends to be exercised later than a traded option with the same terms.

D. Employee stock options are usually exercised as early as possible.

Answer: B Employee stock options tend to be exercised earlier than similar traded options. This is because they cannot be sold and exercising them is the only way to monetize gains. A, C, and D are not true.

2. Which of the following is NOT usually true about employee stock options?

A. There is a vesting period.

B. They can be sold to other employees.

C. They are often at-the-money when issued.

D. Their value is currently a charge to the income statement.

Answer: B Employee stock options cannot be sold. A, C, and D are true.

3. What term is used to describe losses shareholders experience because the interests of managers are not aligned with their own?

A. Agency costs B. Backdating scandals C. Dilution D. Income statement expense Answer: A “Agency costs” refers to costs arising because the interests of managers and shareholders are not aligned.

4. Which of the following are true of employee stock options?

A. They are commonly valued as though they are regular American options.

B. They are commonly valued as though they are regular American options, but with a reduced life.

C. They are commonly valued as though they are regular European option.

D. They are commonly valued as though they are regular European options but with a reduced life.

Answer: D They are commonly valued using Black-Scholes-Merton (i.e., as European options) but with a reduced life to reflect early exercise behavior.

5. Which of the following was true about employee stock options prior to 1995?

A. The options never had any affect on a company’s financial statements.

B. The value of options which were at-the-money when issued had to be expensed on the income statement.

C. The value of options which were at-the-money when issued had to be reported in the notes to the financial statements.

D. Options which were at-the-money when issued did not affect a company’s financial statements.

Answer: D Options which were at the money were assumed to have no cost to a company prior to 1995.

6. Which of the following was true about employee stock options between 1996 and 2004?

A. The options never had any affect on a company’s financial statements.

B. The value of options which were at-the-money when issued had to be expensed on the income statement.

C. The value of options which were at-the-money when issued had to be reported in the notes to the financial statements.

D. Options which were at-the-money when issued did not affect a company’s financial statements.

Answer: C The value of options had to be reported in the notes to the financial statements between 1996 and 2004. They did not have to be expensed.

7. Which of the following was true after 2005?

A. The options never had any affect on a company’s financial statements.

B. The value of options which were at-the-money when issued had to be expensed on the income statement.

C. The value of options which were at-the-money when issued had to be reported in the notes to the financial statements.

D. Options which were at-the-money when issued did not affect a company’s financial statements.

Answer: B After 2005 options had to be expensed on the income statement.

8. Which of the following is true about employee stock options after they have been issued?

A. B. C. D.

They have to be revalued every year.

They have to be revalued every quarter.

They have to be revalued every day like other derivatives.

They never have to be revalued.

Answer: D Options are valued when issued but do not have to be valued subsequently.

9. Which of the following is true about the practice of backdating a stock options grant?

A. It is illegal.

B. It is illegal in the majority of states in the U.S., but not all states.

C. It is illegal in roughly half the states in the U.S. D. It is unethical, but not illegal.

Answer: A Backdating is illegal.

10. A company surprises the market with an announcement that it has granted stock options to senior executives. The options are exercised four years later. When does dilution take place?

A. Dilution takes place when the options are exercised.

B. Dilution takes place on the announcement date.

C. Dilution takes place gradually over the four years.

D. There is no dilution.

Answer: B Efficient markets should ensure that dilution takes place at the time of the announcement.

11. When an employee leaves the company which of the following is usually true?

A. All outstanding employee stock options are forfeited.

B. Out-of-the money employee stock options are forfeited.

C. All options which have vested are forfeited.

D. All options are retained.

Answer: B Usually out-of-the-money options are forfeited and in-the-money options have to be exercised immediately.

12. Which of the following defines the vesting period?

A. The period during which employee stock options can be exercised.

B. The period during which the options are issued.

C. The period during which the strike price of the options equals the stock price.

D. The period during which employee stock options cannot be exercised.

Answer: D

The vesting period is the period during which options cannot be exercised.

13. Which of the following is NOT true?

A. Management has an incentive to issue executive stock options after bad news.

B. Management has an incentive to issue executive stock options before good news.

C. Executive stock options encourage management to pursue strategies that are best for the company in the long run.

D. Management has an incentive to time the announcement of good news just before they plan to exercise their stock options.

Answer: C Executive stock options tend to cause management to have short-term horizons. A, B, and D are not true. This is because management wants to issue options when the price is low and exercise when the price is high.

14. Which of the following strategies makes no sense?

A. An employee exercises stock options early and sells the stock. No dividends are expected.

B. An employee exercises stock options early and keeps the stock. No dividends are expected.

C. An employee exercises stock options early and sells the stock. Dividends are expected.

D. An employee exercises stock options early and keeps the stock. Dividends are expected.

Answer: B An exchange-traded call option on a non-dividend-paying stock should never be exercised early. The only reason for exercising an employee stock option is to monetize it. (The option cannot be sold). But to monetize the option the shares of stock that are obtained must be sold.

15. When a CEO has employee stock options, he or she is in theory motivated to do which of the following?

A. Take more risk B. Take less risk C. Buy some of the company’s stock D. None of the above Answer: A If the CEO takes more risk, volatility increases and the options become more valuable.

16. When an employee stock option is exercised, which of the following is usually true?

A. The employee pays the market price for the shares and the company refunds the difference between the market price and the strike price.

B. The company or the company’s agent buys stock in the market for the employee.

C. The company issues more shares and sells them to the employee for the strike price.

D. The employee cannot immediately sell the shares.

Answer: C When an option is exercised, the company issues more shares and sells them to the employee for the strike price.

17. Which of the following increases the expected life of employee stock options?

A. An increase in the vesting period.

B. An increase in employee turnover.

C. A fast growth rate for the stock price.

D. A tendency for employees to exercise earlier than in the past.

Answer: A If the vesting period increases, employees must wait longer before they are allowed to exercise.

18. Which of the following hypotheses was supported by empirical research covering the 1995 to 2002 period?

A. The grant date for executive stock options tended to be when the stock price is high.

B. The grant date for executive stock options tended to be when the stock price is low.

C. The grant date for executive stock options tended to be after a growth spurt in the stock price.

D. There was no relationship between the timing of grants and the stock price.

Answer: B Empirical research showed that the grant date was a low point for the stock price. This was used as evidence for backdating.

19. Which of the following ensures that managers are rewarded only when a company performs better than its competitors?

A. A constant strike price for executive stock options.

B. A strike price that increases with time.

C. A strike price that changes in line with an index of stock prices.

D. A strike price that is tied to reported profit.

Answer: C If an option is initially at the money and the strike price increases in line with an index, the company must outperform the index for the option to move in the money.

20. Employee stock options are particularly popular with start ups because: A. They encourage employees to work hard.

B. The start up cannot afford to pay high salaries.

C. The risk associated with the company’s success is shared with employees.

D. All of the above.

Answer: D A, B, and C are all reasons why employee stock options are attractive to a start up.

Hull: Options, Futures, and Other Derivatives, Eleventh Edition, Global Edition Chapter 17: Options on Stock Indices and Currencies Multiple Choice Test Bank: Questions with Answers 1. Which of the following describes what a company should do to create a range forward contract in order to hedge foreign currency that will be received?

A. Buy a put and sell a call on the currency with the strike price of the put higher than that of the call.

B. Buy a put and sell a call on the currency with the strike price of the put lower than that of the call.

C. Buy a call and sell a put on the currency with the strike price of the put higher than that of the call.

D. Buy a call and sell a put on the currency with the strike price of the put lower than that of the call.

Answer: B The company wants to ensure that the price received for the foreign currency will be between K1 and K2. It does this by buying a put option with strike price K1 and selling a call option with strike price K2.

2. Which of the following describes what a company should do to create a range forward contract in order to hedge foreign currency that will be paid?

A. Buy a put and sell a call on the currency with the strike price of the put higher than that of the call.

B. Buy a put and sell a call on the currency with the strike price of the put lower than that of the call.

C. Buy a call and sell a put on the currency with the strike price of the put higher than that of the call.

D. Buy a call and sell a put on the currency with the strike price of the put lower than that of the call.

Answer: D The company wants to ensure that the price paid for the foreign currency will be between K1 and K2. It does this by selling a put option with strike price K1 and buying a call option with strike price K2.

3. What should the continuous dividend yield be replaced by when options on an exchange rate are valued using the formula for an option on a stock paying a continuous dividend yield?

A. The domestic risk-free rate.

B. The foreign risk-free rate.

C. The foreign risk-free rate minus the domestic risk-free rate.

D. None of the above.

Answer: B The continuous dividend yield, q, should be replaced by the foreign risk rate, rf.

4. Suppose that the domestic risk free rate is r and dividend yield on an index is q. How should the put-call parity formula for options on a non-dividend-paying stock be changed to provide a putcall parity formula for options on a stock index? Assume the options last T years.

A. The stock price is replaced by the value of the index multiplied by exp(qT).

B. The stock price is replaced by the value of the index multiplied by exp(rT).

C. The stock price is replaced by the value of the index multiplied by exp(−qT).

D. The stock price is replaced by the value of the index multiplied by exp(−rT).

Answer: C S0 is replaced by S0e-qT. 5. A portfolio manager in charge of a portfolio worth $10 million is concerned that stock prices might decline rapidly during the next six months and would like to use put options on an index to provide protection against the portfolio falling below $9.5 million. The index is currently standing at 500 and each contract is on 100 times the index. What position is required if the portfolio has a beta of 1?

A. Short 200 contracts B. Long 200 contracts C. Short 100 contracts D. Long 100 contracts Answer: B The number of contracts required is 10,000,000/(500 × 100) = 200. A long put position is required because the contracts must provide a positive payoff when the market declines.

6. A portfolio manager in charge of a portfolio worth $10 million is concerned that the market might decline rapidly during the next six months and would like to use put options on an index to provide protection against the portfolio falling below $9.5 million. The index is currently standing at 500 and each contract is on 100 times the index. What should the strike price of options on the index be if the portfolio has a beta of 1?

A. 425 B. 450 C. 475 D. 500 Answer: C When the portfolio declines in value by 5%, the index can be expected to decline in value by 5%. The strike price should therefore be 0.95 × 500 = 475.

7. A portfolio manager in charge of a portfolio worth $10 million is concerned that the market might decline rapidly during the next six months and would like to use put options on an index to provide protection against the portfolio falling below $9.5 million. The index is currently standing at 500 and each contract is on 100 times the index. What position is required if the portfolio has a beta of 0.5?

A. Short 200 contracts B. Long 200 contracts C. Short 100 contracts D. Long 100 contracts Answer: C The number of contracts required is 0.5 × 10,000,000/(500 × 100) = 100. A short position is required because the contracts must provide a positive payoff when the market declines.

8. A portfolio manager in charge of a portfolio worth $10 million is concerned that the market might decline rapidly during the next six months and would like to use put options on an index to provide protection against the portfolio falling below $9.5 million. The index is currently standing at 500 and each contract is on 100 times the index. What should the strike price of options on the index be if the portfolio has a beta of 0.5? Assume that the risk-free rate is 10% per annum and there are no dividends.

A. 400 B. 410 C. 420 D. 425 Answer: D The risk-free rate per six months is 5%. When the portfolio declines by 5%, its return per six months is 10% below the risk-free rate. The return on the index is therefore 20% below the risk-free rate. Its return is therefore −15%. The portfolio therefore declines to 500 × 0.85 = 425.

9. For a European put option on an index, the index level is 1,000, the strike price is 1050, the time to maturity is six months, the risk-free rate is 4% per annum, and the dividend yield on the index is 2% per annum. How low can the option price be without there being an arbitrage opportunity?

A. $50.00 B. $43.11 C. $29.21 D. $39.16 Answer: D A lower bound for the put option price is Ke-rT−S0e-qT. In this case, K = 1050, S0 = 1000, T = 0.5, r = 0.04 and q = 0.02. The lower bound is therefore 1050e-0.04×0.5− 1000e-0.02×0.5 = 39.16.

The put price cannot fall below this without there being an arbitrage opportunity.

10. For a European call option on a currency, the exchange rate is 1.0000, the strike price is 0.9100, the time to maturity is one year, the domestic risk-free rate is 5% per annum, and the foreign risk-free rate is 3% per annum. How low can the option price be without there being an arbitrage opportunity?

A. 0.1048 B. 0.0900 C. 0.1344 D. 0.1211 Answer: A A lower bound for the call option price is S 0 e - rf T - Ke - rT . In this case, K = 0.9100, S0 = 1.0000, T = 1, r = 0.05 and rf = 0.03. The lower bound is therefore 1.00e-0.03×1−0.91e-0.05×1 = 0.1048. The call price cannot fall below this without there being an arbitrage opportunity.

11. Index put options are used to provide protection against the value of the portfolio falling below a certain level. Which of the following is true as the beta of the portfolio increases?

A. The cost of hedging increases.

B. The required options have a higher strike price.

C. The number of options required increases.

D. All of the above.

Answer: D As beta increases, A, B, and C are all true.

12. Which of the following is NOT true about a range forward contract?

A. It ensures that the exchange rate for a future transaction will lie between two values.

B. It can be structured so that it costs nothing to set up.

C. It requires a forward contract as well as two options.

D. It can be used to hedge either a future inflow or a future outflow of a foreign currency.

Answer: C A range forward contract requires two options only. A, B, and D are true.

13. A binomial tree with three-month time steps is used to value a currency option. The domestic and foreign risk-free rates are 4% and 6%, respectively. The volatility of the exchange rate is 12%.

What is the probability of an up movement?

A. 0.4435 B. 0.5267

C. 0.5565 D. 0.5771 Answer: A The parameter u is e 0.12 0.25 = 1.0618 and d = 1/u = 0.9418. The probability of an up movement is [e(0.04−0.06)×0.25− 0.9418]/[1.0618 − 0.9418] = 0.4435.

14. A binomial tree with one-month time steps is used to value an index option. The interest rate is 3% per annum and the dividend yield is 1% per annum. The volatility of the index is 16%. What is the probability of an up movement?

A. B. C. D.

0.4704 0.5065 0.5592 0.5833

Answer: B The parameter u is e 0.16 1/12 = 1.0473 and d = 1/u = 0.9549. The probability of an up movement is [e(0.03−0.01)×1/12− 0.9549]/[1.0473 − 0.9549] = 0.5065.

15. A European at-the-money call option on a currency has four years until maturity. The exchange rate volatility is 10%, the domestic risk-free rate is 2% and the foreign risk-free rate is 5%. The current exchange rate is 1.2000. What is the value of the option?

A. 0.98N(0.25) − 1.11(0.05) B. 0.98N(−0.3) − 1.11N(−0.5) C. 0.98N(−0.5) − 1.11N(−0.7) D. 0.98N(0.10) − 1.11N(0.06) Answer: C The formula is -r T

c = S 0 e f N (d1 ) - Ke - rT N (d 2 ) d1 = In this case S0 e

d1 =

ln(S 0 / K ) + (r - rf + s 2 / 2)T s T - rf T

d 2 = d1 - s T

= 1.2e-0.05´4 = 0.9825 and Ke - rT = 1.2e -0.02´4 = 1.1077

ln(1) + (0.02 - 0.05 + 0.12 / 2)4 = -0.5 0.1 4

The correct answer is therefore C.

d 2 = d1 - s T = -0.7

16. A European at-the-money put option on a currency has four years until maturity. The exchange rate volatility is 10%, the domestic risk-free rate is 2% and the foreign risk-free rate is 5%. The current exchange rate is 1.2000. What is the value of the option?

A. 1.11N(0.7) − 0.98N(0.5) B. 1.11N(−0.7) − 0.98N(−0.5) C. 1.11N(0.7) − 0.98N(0.4) D. 1.11N(−0.06) − 0.98N(−0.10) Answer: A The formula is -r T

p = Ke - rT N (-d 2 ) - S0e f N (-d1 ) d1 =

ln(S0 / K ) + (r - rf + s2 / 2)T

d 2 = d1 - s T s T -r T In this case S0 e f = 1.2e -0.05´4 = 0.9825 and Ke - rT = 1.2e -0.02´4 = 1.1077

d1 =

ln(1) + (0.02 - 0.05 + 0.12 / 2)4 = -0.5 0.1 4

d 2 = d1 - s T = -0.7

The correct answer is therefore A. 17. Which of the following is true when a European currency option is valued using forward exchange rates?

A. It is not necessary to know the domestic interest rate or the spot exchange rate.

B. It is not necessary to know either the foreign or domestic interest rate.

C. It is necessary to know the difference between the foreign and domestic interest rates but not the rates themselves.

D. It is not necessary to know the foreign interest rate or the spot exchange rate.

Answer: D The forward exchange rate contains all the information necessary about the foreign risk-free interest rate and the spot exchange rate. It is still necessary to know the domestic risk-free interest rate.

18. What is the size of one option contract on the S&P 500?

A. 250 times the index B. 100 times the index C. 50 times the index D. 25 times the index Answer: B One option is on 100 times the index.

19. The domestic risk-free rate is 3%. The foreign risk-free rate is 5%. What is the risk-neutral growth rate of the exchange rate?

A. +2% B. −2% C. +5% D. +3% Answer: B The growth rate is 3% minus 5% or −2%.

20. What is the same as 100 call options to buy one unit of currency A with currency B at a strike price of 1.25?

A. 100 call options to buy one unit of currency B with currency A at a strike price of 0.8.

B. 125 call options to buy one unit of currency B with currency A at a strike price of 0.8.

C. 100 put options to sell one unit of currency B for currency A at a strike price of 0.8.

D. 125 put options to sell one unit of currency B for currency A at a strike price of 0.8.

Answer: D Buying 100 units of A with 125 units of B is the same a selling 125 units of B for 100 units of A.

Hull: Options, Futures, and Other Derivatives, Eleventh Edition, Global Edition Chapter 18: Futures Options and Black’s Model Multiple Choice Test Bank: Questions with Answers 1. Which of the following is acquired (in addition to a cash payoff) when the holder of a put futures exercises?

A. A long position in a futures contract.

B. A short position in a futures contract.

C. A long position in the underlying asset.

D. A short position in the underlying asset.

Answer: B The holder of the put acquires a short futures position which can be immediately closed out if desired.

2. Which of the following is acquired (in addition to a cash payoff) when the holder of a call futures exercises?

A. A long position in a futures contract.

B. A short position in a futures contract.

C. A long position in the underlying asset.

D. A short position in the underlying asset.

Answer: A The holder of the call acquires a long futures position which can be immediately closed out if desired.

3. The risk-free rate is 5% and the dividend yield on the S&P 500 index is 2%. Which of the following is correct when a futures option on the index is being valued?

A. The futures price of the S&P 500 is treated like a stock paying a dividend yield of 5%.

B. The futures price of the S&P 500 is treated like a stock paying a dividend yield of 2%.

C. The futures price of the S&P 500 is treated like a stock paying a dividend yield of 3%.

D. The futures price of the S&P 500 is treated like a non-dividend-paying stock.

Answer: A When a futures option is being valued, the dividend yield is set equal to the domestic risk-free rate. In this case, the domestic risk-free rate is 5%. A is therefore correct.

4. Which of the following is NOT true?

A. Black’s model can be used to value an American-style option on futures.

B. Black’s model can be used to value a European-style option on futures.

C. Black’s model can be used to value a European-style option on spot.

D. Black’s model is widely used by practitioners.

Answer: A Black’s model is used for valuing European options. A is therefore clearly false.

5. Which of the following is true when the futures price exceeds the spot price?

A. Calls on futures should never be exercised early.

B. Put on futures should never be exercised early.

C. A call on futures is always worth at least as much as the corresponding call on spot.

D. A call on spot is always worth at least as much as the corresponding call on futures.

Answer: C If the futures price is above the spot price, a call on futures must be worth more than a call on spot. Both calls and puts on futures are sometimes exercised early.

6. Which of the following describes a futures-style option?

A. An option on a futures B. An option on spot with daily settlement C. A futures on an option payoff D. None of the above Answer: C A futures style option is a futures contract on the option payoff.

7. A futures price is currently 40 cents. It is expected to move up to 44 cents or down to 34 cents in the next six months. The risk-free interest rate is 6%. What is the probability of an up movement in a risk-neutral world?

A. 0.4 B. 0.5 C. 0.72 D. 0.6 Answer: D The probability of an up movement is (1 − d)/(u − d). In this case, u is 1.1 and d is 0.85. The probability of an up movement is therefore 0.15/0.25 = 0.6.

8. A futures price is currently 40 cents. It is expected to move up to 44 cents or down to 34 cents in the next six months. The risk-free interest rate is 6%. What is the value of a six-month put option with a strike price of 37 cents?

A. 3.00 cents B. 2.91 cents C. 1.16 cents D. 1.20 cents

Answer: C The probability of an up movement is (1 − d)/(u − d). In this case u is 1.1 and d is 0.85. The probability of an up movement is therefore 0.15/0.25 = 0.6. The option pays off zero if there is an up movement and 3 cents if there is a down movement. The value of the option is therefore 0.4 × 3 × e-0.06×0.5= 1.16 cents.

9. A futures price is currently 40 cents. It is expected to move up to 44 cents or down to 34 cents in the next six months. The risk-free interest rate is 6%. What is the value of a six month call option with a strike price of 39 cents?

A. 5.00 cents B. 2.91 cents C. 3.00 cents D. 4.21 cents Answer: B The probability of an up movement is (1−d)/(u−d). In this case u is 1.1 and d is 0.85. The probability of an up movement is therefore 0.15/0.25 = 0.6. The option pays off 5 cents if there is an up movement and zero if there is a down movement. The value of the option is therefore 0.6 × 5 × e-0.06×0.5 = 2.91 cents.

10. Which of the following are true?

A. Futures options are usually European.

B. Futures options are usually American.

C. Both American and European futures options trade actively in exchanges.

D. Both American and European futures options trade actively in the OTC market.

Answer: B Futures options trade on exchanges and are American.

11. Which of the following is true for a September futures option?

A. The expiration month of option is September.

B. The option was first traded in September.

C. The delivery month of the underlying futures contract is September.

D. September is the first month when the option can be exercised.

Answer: C The month of a futures option refers to the month of the underlying futures contract.

12. What is the cash settlement if a put futures option on 50 units of the underlying asset is exercised?

A. (Current Futures Price – Strike Price) times 50 B. (Strike Price – Current Futures Price) times 50

C. (Most Recent Futures Settlement Price – Strike Price) times 50 D. (Strike Price – Most Recent Futures Settlement Price) times 50 Answer: D The cash payoff is the strike price minus the most recent futures settlement price times the size of the contract. The party exercising also gets a short futures position which brings the value of what is received at the time of exercise equal to strike price minus the current futures price times the size of the contract.

13. What is the cash component of the payoff if a call futures option on 50 units of the underlying asset is exercised?

A. (Current Futures Price – Strike Price) times 50 B. (Strike Price – Current Futures Price) times 50 C. (Most Recent Futures Settlement Price – Strike Price) times 50 D. (Strike Price – Most Recent Futures Settlement Price) times 50 Answer: C When the option is exercised, the holder obtains the cash payoff in C and a long futures contract.

14. Which of the following is true?

A. A stock option is settled daily.

B. A futures-style option is settled daily.

C. A foreign currency option is settled daily.

D. None of the above.

Answer: B A futures style like a futures contract is settled daily. Regular options are not settled daily.

15. Which of the following is true about a futures option and a spot option on the same underlying asset when they have the same strike price? The expiration dates of the two options and the futures are all the same.

A. A European call spot option and an American call futures option are equivalent.

B. An American call spot option and a European call futures option are equivalent.

C. A European put spot option and European put futures option are equivalent.

D. An American put spot option and American put futures option are equivalent.

Answer: C The two European options are equivalent. This result is often used to price options on spot.

16. What is the value of a European call futures option where the futures price is 50, the strike price is 50, the risk-free rate is 5%, the volatility is 20% and the time to maturity is three months?

A. 49.38N(0.05) – 49.38N(–0.05)

B. 50N(0.05) –50N(–0.05) C. 49.38N(0.1) –49.38N(–0.1) D. 50N(0.1) –49.38N(–0.1) Answer: A The formula is

c = F0e- rT N (d1 ) - Ke - rT N (d 2 ) ln( F0 / K ) + s2T / 2 d1 = s T

d 2 = d1 - s T

In this case Ke - rT = F0e - rT = 50e -0.05´0.25 = 48.38

d1 =

ln(1) + 0.22 ´ 0.25 / 2 = 0.05 0.2 0.25

d2 = d1 - s T = -0.05

The correct answer is therefore A. 17. What is the expected growth rate of an index futures price in the risk-neutral world?

A. The excess of the risk-free rate over the dividend yield B. The risk-free rate C. The dividend yield on the index D. Zero Answer: D All futures prices grow at rate zero on average in a risk-neutral world.

18. When Black’s model is used to value a European option on the spot price of an asset, which of the following is NOT true?

A. It is necessary to know the futures or forward price for a contract maturing at the same time as the option.

B. It is not necessary to estimate income on the underlying asset.

C. It is not necessary to know the risk-free rate.

D. The underlying asset can be an investment or a consumption asset.

Answer: C The futures price embodies all the relevant information needed about the spot price and the income on the asset. However, it is still necessary to know the risk-free rate.

19. Consider a European one-year call futures option and a European one-year put futures options when the futures price equals the strike price. Which of the following is true?

A. The call futures option is worth more than the put futures option.

B. The put futures option is worth more than the call futures option.

C. The call futures option is sometimes worth more and sometimes worth less than the put

futures option.

D. The call futures option is worth the same as the put futures option.

Answer: D Put call parity is c + Ke-rT = p + F0e-rT When F0 = K it follows that c = p.

20. One-year European call and put options on an asset are worth $3 and $4, respectively, when the strike price is $20 and the one-year risk-free rate is 5%. What is the one-year futures price of the asset if there are no arbitrage opportunities? (Use put-call parity.)

A. $19.55 B. $18.95 C. $20.95 D. $20.45 Answer: B Put call parity is c + Ke-rT = p + F0e-rT Hence F0 = K + (c – p)erT = 20 + (3 – 4)e0.05×1= $18.95

Hull: Options, Futures, and Other Derivatives, Eleventh Edition, Global Edition Chapter 19: The Greek Letters Multiple Choice Test Bank: Questions with Answers 1. A call option on a stock has a delta of 0.3. A trader has sold 1,000 options. What position should the trader take to hedge the position?

A. Sell 300 shares B. Buy 300 shares C. Sell 700 shares D. Buy 700 shares Answer: B When the stock price increases by a small amount, the option price increases by 30% of this amount. The trader therefore has a hedged position if he or she buys 300 shares. For small changes, the gain or loss on the stock position is equal and opposite to the loss or gain on the option position.

2. What does theta measure?

A. The rate of change of delta with the asset price.

B. The rate of change of the portfolio value with the passage of time.

C. The sensitivity of a portfolio value to interest rate changes.

D. None of the above.

Answer: B Theta measures the rate of change in the value of a portfolio with the passage of time.

3. What does gamma measure?

A. The rate of change of delta with the asset price.

B. The rate of change of the portfolio value with the passage of time.

C. The sensitivity of a portfolio value to interest rate changes.

D. None of the above.

Answer: A Gamma measures the rate of change of delta with the asset price.

4. What does vega measure?

A. The rate of change of delta with the asset price.

B. The rate of change of the portfolio value with the passage of time.

C. The sensitivity of a portfolio value to interest rate changes.

D. None of the above.

Answer: D Vega measures the rate of change of the value of the portfolio value with volatility.

5. What does rho measure?

A. The rate of change of delta with the asset price.

B. The rate of change of the portfolio value with the passage of time.

C. The sensitivity of a portfolio value to interest rate changes.

D. None of the above.

Answer: C Rho measures the rate of change of the value of the portfolio with interest rates. (Usually a parallel shift in interest rates is considered.)

6. Which of the following is true?

A. The delta of a European put equals minus the delta of a European call.

B. The delta of a European put equals the delta of a European call.

C. The gamma of a European put equals minus the gamma of a European call.

D. The gamma of a European put equals the gamma of a European call.

Answer: D The delta of a put on a non-dividend-paying stock equals the delta of the call minus one. The gamma of a put equals the gamma of call even when there are dividends.

7. A portfolio of derivatives on a stock has a delta of 2400 and a gamma of –10. An option on the stock with a delta of 0.5 and a gamma of 0.04 can be traded. What position in the option is necessary to make the portfolio gamma neutral?

A. Long position in 250 options B. Short position in 250 options C. Long position in 20 options D. Short position in 20 options Answer: A The options must have a gamma of +10 to neutralize the gamma of the portfolio. Each option has a gamma of 0.04. Hence a long position of 10/0.04 = 250 options is required.

8. A trader uses a stop-loss strategy to hedge a short position in a three-month call option with a strike price of 0.7000 on an exchange rate. The current exchange rate is 0.6950 and value of the option is 0.1. The trader covers the option when the exchange rate reaches 0.7005 and uncovers (i.e., assumes a naked position) if the exchange rate falls to 0.6995. Which of the following is NOT true?

A. The exchange rate trading might cost nothing so that the trader gains 0.1 for each option sold.

B. The exchange rate trading might cost considerably more than 0.1 for each option sold so that the trader loses money.

C. The present value of the gain or loss from the exchange rate trading should be about 0.1 on average for each option sold.

D. The hedge works reasonably well.

Answer: D A good hedging system will ensure that the cost of selling an option is close to its theoretical value. The stop-loss hedging procedure does not have this property. It can lead to the option costing nothing or costing considerably more than its theoretical value. On average, the cost of the option is its Black–Scholes value, but there is a wide variation. D is the correct answer.

9. Maintaining a delta-neutral portfolio is an example of which of the following?

A. Stop-loss strategy B. Dynamic hedging C. Hedge and forget strategy D. Static hedging Answer: B Delta-neutral hedging is an example of dynamic hedging. The hedge has to be adjusted periodically. (In theory, to maintain a delta-neutral hedge, the hedge must be adjusted continuously.)

10. Which of the following could NOT be a delta-neutral portfolio?

A. A long position in call options plus a short position in the underlying stock.

B. A short position in call options plus a short position in the underlying stock.

C. A long position in put options and a long position in the underlying stock.

D. A long position in a put option and a long position in a call option.

Answer: B Calls have a positive delta. Puts have a negative delta. A long stock position has a positive delta.

A short stock position has a negative delta. B cannot be delta neutral (i.e., have a delta of zero) because both parts of the portfolio have a negative delta.

11. Which of the following is NOT true about gamma?

A. A highly positive or highly negative value of gamma indicates that a portfolio needs frequent rebalancing to stay delta neutral.

B. The magnitude of gamma is a measure of the curvature of the portfolio value as a function of the underlying asset price.

C. A big positive value for gamma indicates that a big movement in the asset price in either direction will lead to a loss.

D. A long position in either a call or a put has a positive gamma.

Answer: C C is not true. The change in the value is a gain of 0.5GDS2. There is a gain from a big movement when gamma is positive and a loss from a big movement when gamma is negative.

12. Gamma tends to be high for which of the following?

A. At-the money options B. Out-of-the money options C. In-the-money options D. Options with a long time to maturity Answer: A Gamma tends to be high for at-the-money options. See Figure 19.9.

13. Which of the following is true for a call option on a non-dividend-paying stock when the stock’s price equals the strike price?

A. It has a delta of 0.5.

B. It has a delta less than 0.5.

C. It has a delta greater than 0.5.

D. Delta can be greater than or less than 0.5.

Answer: C The delta is N(d1) where

ln(S0 / K ) + (r + s2 / 2)T d1 = s T From this it can be seen that, when S0 = K, d1 is

( r + s 2 / 2) T s

This is always positive. Hence, delta is always greater than 0.5.

14. The risk-free rate is 5% and the dividend yield on an index is 2%. Which of the following is the delta with respect to the index for a one-year futures on the index?

A. 0.98 B. 1.05

C. 1.03 D. 1.02 Answer: C The futures price is given by

F0 = S0e(r-q)T Hence, the delta of the futures with respect to the spot is e(r-q)T. In this case, this is e(0.05-0.03)×1 = 1.03 15. The gamma of a delta-neutral portfolio is 500. What is the impact of a jump of $3 in the price of the underlying asset?

A. A gain of $2,250 B. A loss of $2,250 C. A gain of $750 D. A loss of $750 Answer: A The change in the value is a gain of 0.5GDS2 = 0.5 × 500 × 32 = $2,250.

16. Vega tends to be high for which of the following?

A. At-the money options B. Out-of-the money options C. In-the-money options D. Options with a short time to maturity Answer: A Vega tends to be high for at-the-money options. See Figure 19.11.

17. The delta of a call option on a non-dividend-paying stock is 0.4. What is the delta of the corresponding put option?

A. –0.4 B. 0.4 C. –0.6 D. 0.6 Answer: C The delta of a call option is N(d1) and the delta of a put is N(d1)−1. When N(d1) = 0.4, N(d1)−1 is −0.6.

18. A call option on a non-dividend-paying stock has a strike price of $30 and a time to maturity of six months. The risk-free rate is 4% and the volatility is 25%. The stock price is $28. What is the

delta of the option?

A. N(–0.1342) B. N(–0.1888) C. N(–0.2034) D. N(–0.2241) Answer: B The delta is N(d1) where

d1 =

ln(S0 / K ) + (r + s2 / 2)T s T

In this case

d1 =

ln(28 / 30) + (0.04 + 0.252 / 2) ´ 0.5 = -0.1888 0.25 0.5

19. Which of the following is NOT a letter in the Greek alphabet?

A. delta B. rho C. vega D. gamma Answer: C Vega, although it is referred to a “Greek letter” by option traders, is not a letter in the Greek alphabet.

20. Which of the following is true for a long position in an option?

A. Both gamma and vega are negative.

B. Gamma is negative and vega is positive.

C. Gamma is positive and vega is negative.

D. Both gamma and vega are positive.

Answer: D Gamma and vega are both positive for a long position in an option. It does not matter whether the option is a call or a put.

Hull: Options, Futures, and Other Derivatives, Eleventh Edition, Global Edition Chapter 20: Volatility Smiles and Volatility Surfaces Multiple Choice Test Bank: Questions with Answers 1. Which of the following is true of a volatility smile?

A. Implied volatility is on the horizontal axis and strike price is on the vertical axis.

B. Historical volatility is on the horizontal axis and strike price is on the vertical axis.

C. Implied volatility is on the vertical axis and strike price is on the horizontal axis.

D. Historical volatility is on the vertical axis and strike price is on the horizontal axis.

Answer: C A volatility smile shows implied volatility (which is on the vertical axis) as a function of the strike price (which is on the horizontal axis).

2. Which of the following is true?

A. Volatility smile for European puts is the same as for European calls.

B. Volatility smile for European puts is the same as for American puts.

C. Volatility smile for European calls is the same as for American calls.

D. Volatility smile for American puts is the same as for American calls.

Answer: A Put call parity shows that the volatility smile for European puts should be exactly the same as that for European calls. The volatility smile for American options is usually close to but not exactly the same as that for European options.

3. Which of the following is true when the tails of a future foreign currency distribution are compared with those of a lognormal distribution with the same mean and standard deviation?

A. The left tail and right tail are thinner.

B. The left tail is thinner and the right tail is fatter.

C. The right tail is thinner and the left tail is fatter.

D. Both tails are fatter.

Answer: D Both tails of the foreign currency distribution are fatter. This leads to a U-shaped smile.

4. Which of the following is true when the tails of a future stock price distribution are compared with those of a lognormal distribution with the same mean and standard deviation?

A. The left tail and right tail are thinner.

B. The left tail is thinner and the right tail is fatter.

C. The right tail is thinner and the left tail is fatter.

D. Both tails are fatter.

Answer: C

The left tail is fatter and the right tail is thinner.

5. Which of the following could cause the volatility smile typically seen for foreign currency options?

A. Currencies are traded in different countries at different times of the day.

B. Currencies tend to have low volatilities.

C. The activities of central banks causes occasional jumps in the exchange rate.

D. Interest rates may be different in the two countries.

Answer: C The possibility of jumps in the exchange rate makes extreme exchange rates more likely and is consistent with the volatility smile that is observed.

6. Which of the following is true?

A. The volatility skew for equities is much more pronounced now than it was in 1985.

B. The volatility skew for equities has a positive gradient.

C. The volatility skew for equities is consistent with the Black–Scholes–Merton model.

D. The volatility skew for equities is similar to that for foreign currencies.

Answer: A There was very little volatility skew or smile for equities prior to the crash of 1987.

7. Why do traders use volatility smiles for pricing options?

A. To allow for non-lognormality of the probability distribution of future asset price.

B. Because it is consistent with recent market moves.

C. As a tool to reflect their views about extreme market moves.

D. Because extreme market moves are always more likely than Black–Scholes–Merton assumes.

Answer: A Volatility smiles allow for the fact that the assumptions underlying the Black–Scholes–Merton model do not hold exactly. The BSM assumptions imply a lognormally distributed future asset price.

8. What does the shape of the volatility smile reveal about put options on equity?

A. Options close-to-the-money have the lowest implied volatility.

B. Options deep-in-the-money have a relatively high implied volatility.

C. Options deep-out-of-the-money have a relatively high implied volatility.

D. All of the above.

Answer: C

The volatility smile shows that low-strike-price options have high implied volatilities relative to at-the-money options. High-strike-price options have low implied volatilities relative to at-themoney options. Out-of-the-money put options have a low strike price. Hence C is correct.

9. What does the shape of the volatility smile reveal about call options on a currency?

A. Options close-to-the-money have the lowest implied volatility.

B. Options deep-in-the-money have a relatively high implied volatility.

C. Options deep-out-of-the-money have a relatively high implied volatility.

D. All of the above.

Answer: D D is correct. The volatility smile for currency options is U-shaped.

10. Which of the following is NOT true?

A. A volatility surface provides more information than a single volatility smile.

B. A volatility surface is used to determine the implied volatility of an option that does not trade actively.

C. A volatility surface can be determined from a single volatility smile using interpolation.

D. A volatility surface incorporates information about options with different maturity dates.

Answer: C A volatility surface requires a knowledge of how implied volatilities vary with option maturity. C is therefore not true.

11. A volatility surface is a table showing the relationship among which of the following?

A. Implied volatility, time to maturity, and strike price B. Implied volatility, historical volatility, and time to maturity C. Historical volatility, strike price, and time to maturity D. None of the above Answer: A A volatility surface is a look-up table showing implied volatilities as a function of strike price and time to maturity.

12. Which of the following causes a volatility smile that is a “frown”?

A. There is a small probability of a large stock price decrease in one week.

B. There is a small probability of a large stock price increase in one week.

C. The outcome of a lawsuit (roughly equal chance of being favorable or unfavorable) will create a large movement up or down in one week.

D. None of the above.

Answer: C As shown at the end of the chapter, the situation in C leads to a “frown”.

13. Which of the following could be a result of “crashophobia”?

A. High volatilities for in-the-money calls B. High volatilities for in-the-money puts C. High volatilities for at-the-money calls D. Low volatilities for at-the-money puts Answer: A Crashophobia is the word used to describe a possible “phobia” that traders might have that the market will crash. It would lead to out-of-the-money put options with low strike prices having high values and therefore high implied volatilities. In-the-money call options have the same implied volatilities as the corresponding out-of-the-money put options. Hence, they also have high implied volatilities and the correct answer is A. 14. Which of the following is true for European call and put options?

A. If they have the same strike price, they have the same implied volatility.

B. If they have the same time to maturity, they have the same implied volatility.

C. If they have the same strike price and time to maturity, they have the same implied volatility.

D. None of the above.

Answer: C If a European call and put option have the same strike price and time to maturity put-call parity shows that they must have the same implied volatility. Otherwise there are arbitrage opportunities.

15. Which of the following is true about daily exchange rate moves?

A. Four standard deviation daily moves in an exchange rate happen less frequently than they would do if changes were normally distributed.

B. Four standard deviation daily movements in an exchange rate happen more frequently than three standard deviation moves in the exchange rate.

C. The frequency of six standard deviation daily movements in an exchange rate is about once every 100 years.

D. None of the above.

Answer: D A, B, and C are not true. Large daily exchange rate moves happen more frequently than they would if they were normally distributed. By definition, a four-standard deviation move occurs less frequently than a three-standard deviation move. A six-standard deviation move happens

more frequently than once every 100 years. The table in the text suggests the probability is 3/10,000. Given that there are 250 business days in a day, this is about once every 13 years.

16. The daily percentage change in an exchange rate is compared to a normal distribution with the same mean and standard deviation. Which of the following is true?

A. Both small and large exchange rate moves are more likely than with the normal distribution.

B. Small exchange rate moves are less likely and large exchange rate moves are more likely than with the normal distribution.

C. Large exchange rate moves are less likely and small exchange rate moves are more likely than with the normal distribution.

D. Both small and large exchange rate moves are less likely than with the normal distribution.

Answer: A Both large and small movements in the exchange rate happen more often than the normal distribution would predict.

17. Which of the following is true as time to maturity increases?

A. The volatility smile for currency options tends to become more pronounced.

B. The volatility smile for currency options tends to become less pronounced.

C. The volatility smile for currency options first becomes less pronounced and then becomes more pronounced.

D. The volatility smile for currency options remains approximately the same.

Answer: B The volatility smile tends to become less pronounced as the time to maturity increases. (This does not mean that its impact on prices becomes less pronounced.)

18. If the volatility implied from an at-the-money put currency option were used to price other put options on the currency, which of the following would be true?

A. Out-of-the money and in-the-money prices would be too high.

B. Out-of-the money and in-the-money prices would be too low.

C. Out-of-the-money option prices would be too high and in-the-money option prices would be too low.

D. Out-of-the-money option prices would be too low and in-the-money option prices would be too high.

Answer: B The volatility smile for currency options shows that at-the-money options have lower implied volatilities than out-of-the-money and in-the-money options. This means that using at-the-

money implied volatilities for out-of-the-money or in-the-money options would lead to the volatility being too low so that there would be underpricing.

19. If the volatility implied from an at-the-money put stock option were used to price other put options on the stock, which of the following would be true?

A. Out-of-the money and in-the-money prices would be too high.

B. Out-of-the money and in-the-money prices would be too low.

C. Out-of-the-money option prices would be too high and in-the-money option prices would be too low.

D. Out-of-the-money option prices would be too low and in-the-money option prices would be too high.

Answer: D The volatility smile for equity options shows that at-the-money put options have lower implied volatilities than out-of-the-money put options and a higher volatility than in-the-money put options. This means that using at-the-money implied volatilities for out-of-the-money put options would lead to underpricing and using at-the-money implied volatilities for in-the-money put options would lead to overpricing . Hence, the correct answer is D.

20. The implied volatilities for strike prices of 1.1 and 1.2 when the time to maturity is 6 months are 20% and 22%. The implied volatilities for strike prices of 1.1 and 1.2 when the time to maturity is 1 year are 18.8% and 20.2%. Using linear interpolation, what is the implied volatility for a strike price of 1.12 and a time to maturity of 10 months?

A. 19.24% B. 19.52% C. 20.48% D. 19.96% Answer: B This involves a two-dimensional interpolation. We can either interpolate between strike prices first and then interpolate between maturities, or the other way round. Suppose we interpolate between strike prices first. We get the implied volatility for a 6-month option with a time to maturity of 6 months and a strike price of 1.12 as 0.8 × 20 + 0.2 × 22 = 20.4%. Similarly, we get the implied volatility for a 1 year option and a strike price of 1.12 as 0.8 × 18.8 + 0.2 × 20.2 = 19.08%. We next interpolate between maturities to get the volatility for a 10 month option with a strike price of 1.12 as 0.33 × 20.4 + 0.66 × 19.08 = 19.52%. If you chose to interpolate between maturities first and then between strike prices, you should have got the same answer!

Hull: Options, Futures, and Other Derivatives, Eleventh Edition, Global Edition Chapter 21: Basic Numerical Procedures Multiple Choice Test Bank: Questions with Answers 1. How many nodes are there at the end of a Cox–Ross–Rubinstein five-step binomial tree?

A. 4 B. 5 C. 6 D. 7 Answer: C The number of nodes at the end of one-time step is 2; the number of nodes at the end of two-time steps is 3; and so on.

2. Which of the following cannot be estimated from a single binomial tree?

A. delta B. gamma C. theta D. vega Answer: D To calculate vega, it is necessary to increase volatility slightly and construct a new tree. The other three can be estimated from a single tree.

3. Which of the following is true for u in a Cox–Ross–Rubinstein binomial tree?

A. It depends on the interest rate and the volatility.

B. It depends on the volatility but not the interest rate.

C. It depends on the interest rate but not the volatility.

D. It depends on neither the interest rate nor the volatility.

Answer: B

u = es Dt . It therefore depends on volatility but not the interest rate.

4. How many different paths are there through a Cox–Ross–Rubinstein tree with four-steps?

A. 5 B. 9 C. 12 D. 16 Answer: D

There are two choices for the path chosen at the initial node, two choices at the node reached at the end of the first time step, and so on. The total number of paths is 24 = 16.

5. When we move from assuming no dividends to assuming a constant dividend yield, which of the following is true for a Cox–Ross–Rubinstein tree?

A. The parameters u and p change.

B. p changes but u does not.

C. u changes but p does not.

D. Neither p nor u changes.

Answer: B The formula for u does not change but the formula for p does change.

6. When the stock price is 20 and the present value of dividends is 2, which of the following is the recommended way of constructing a tree?

A. Draw a tree for an initial stock price of 20 and subtract the present value of future dividends at each node.

B. Draw a tree for an initial stock price of 22 and subtract the present value of future dividends at each node.

C. Draw a tree with an initial stock price of 18 and add the present value of future dividends at each node.

D. Draw a tree with an initial stock price of 18 and add 2 at each node.

Answer: C We first subtract the present value of dividends from the initial stock price. We then draw the tree and then add back the present value of future dividends at each node.

7. What is the recommended way of making interest rates a function of time in a Cox–Ross– Rubinstein tree?

A. Make u a function of time.

B. Make p a function of time.

C. Make u and p a function of time.

D. Make the lengths of the time steps unequal.

Answer: B u does not depend on interest rates but p does. The impact of the interest rate being a function of time is therefore to make p a function of time.

8. What is the recommended way of making volatility a function of time in a Cox–Ross–Rubinstein tree?

A. Make u a function of time.

B. Make p a function of time.

C. Make u and p a function of time.

D. Make the lengths of the time steps unequal.

Answer: D To make volatility a function of time, we make the lengths of time steps inversely proportional to variance.

9. A binomial tree prices an American option at $3.12 and the corresponding European option at $3.04. The Black–Scholes–Merton price of the European option is $2.98. What is the control variate price of the American option?

A. $3.06 B. $3.18 C. $2.90 D. $3.08 Answer: A The control variate price is 3.12 + (2.98 – 3.04) = 3.06.

10. The chapter discusses an alternative to the Cox–Ross–Rubinstein tree. In this alternative, which of the following are true?

A. The relationship between u and d is: u = 1/d B. The relationship between u and d is: u – 1 = 1 – d C. The probabilities on the tree are all 0.5 D. None of the above Answer: C Instead of using a degree of freedom to set u = 1/d (as is done in CRR), the alternative method uses a degree of freedom to set both the up and down probabilities to 0.5.

11. Which of the following cannot be valued by Monte Carlo simulation?

A. European options B. American options C. Asian options (i.e., options on the average stock price) D. An option which provides a payoff of $100 if the stock price is greater than the strike price at maturity.

Answer: B American options cannot be valued in a simple way using Monte Carlo simulation because Monte Carlo simulation works forward from the beginning of the life of an option and we do not know whether the option should be exercised when a particular time is reached.

12. Which of the following is true?

A. The implicit finite difference method relates prices at one node to three prices at nodes at a later time.

B. The implicit finite difference method relates prices at one node to three prices at nodes

at an earlier time.

C. The implicit finite difference method relates prices at one node to three prices at nodes at the same time.

D. None of the above.

Answer: B The implicit finite difference relates prices at time t to three prices at nodes at time t−Dt. 13. Which of the following is true?

A. The implicit finite difference method is equivalent to using a trinomial tree.

B. The explicit finite difference method is equivalent to using a trinomial tree.

C. Both methods are equivalent to using a trinomial tree.

D. Neither method is equivalent to using a trinomial tree.

Answer: B The explicit finite difference method is equivalent to using a trinomial tree. The implicit finite difference method is equivalent to using a multinomial tree.

14. The standard deviation of the values of an option calculated using 10,000 Monte Carlo trials is 4.5. The average of the values is 20. What is the standard error of this as an estimate of the option price?

A. 4.5 B. 0.45 C. 0.045 D. 0.0045 Answer: C The standard deviation of 20 as an estimate of the price is the standard deviation of the calculated values divided by the square root of the number of trials. In this case, the square root of the number of trials is 100 and so the standard error of the price estimate is 4.5/100 or 0.045.

15. The values of a stock price at the end of the second time step are $80, $100, $125. The corresponding values of an option are $0, $5, and $20, respectively. What is an estimate of gamma?

A. 0.136 B. 0.146 C. 0.156 D. 0.166 Answer: C

The two delta estimates are (5 − 0)/(100 – 80) = 0.25 and (20 – 5)/125 – 100) = 0.6. The mid points of the ranges over which these are calculated are 90 and 112.5.The gamma estimate is therefore (0.6 – 0.25)/(112.5 – 90) = 0.156.

16. What is the difference between valuing an American and a European option using a tree?

A. The value of u is higher for American options.

B. The value of u is lower for American options.

C. The time steps for American options are not equal.

D. It is necessary to do two calculations at nodes where the option is in the money.

Answer: D When valuing American options, it is necessary to calculate at each in-the-money node how much the option is worth if it is exercised (i.e., the intrinsic value at the node) and how much it is worth if it is not exercised (i.e., the roll back value).

17. A European option on a stock with a known dollar dividend is valued by setting the stock price variable equal to the stock price minus the present value of the dividend in the Black–Scholes– Merton formula. A second price can be obtained using the tree building procedure in the chapter. Which of the following is true when a very large number of time steps are used in the tree?

A. The first price is higher than the second price.

B. The first price is lower than the second price.

C. The first price is sometimes higher and sometimes lower than the second price.

D. The two prices are almost exactly the same.

Answer: D The two prices are exactly the same because they are based on treating dividends in the same way.

18. Which of the following is possible in a modified Cox–Ross–Rubinstein binomial tree?

A. The interest rate and volatility can both be functions of time.

B. The interest rate or the volatility can be a function of time, but not both.

C. The interest rate can be a function of time but the volatility cannot.

D. The interest rate and volatility must be constant.

Answer: A Both the Dt-period interest rate and the volatility can be made functions of time as described in the text.

19. Which of the following describes the way that the parameters in a binomial tree are chosen?

A. The expected return during each time step is the risk-free rate.

B. The standard deviation of the return in each time step is, for small time steps, almost

exactly equal to the volatility per annum times the square root of the length of the time step in years.

C. The tree recombines.

D. All of the above.

Answer: D A, B, and C are all true.

20. Which of the following can be valued without using a numerical procedure such as a binomial tree?

A. American put options on a non-dividend paying stock.

B. American call options on a non-dividend paying stock.

C. American call options on a currency.

D. American put options on futures.

Answer: B The answer is B because an American call on a non-dividend paying stock is worth the same as the corresponding European call, which can be valued with BSM.

Hull: Options, Futures, and Other Derivatives, Eleventh Edition, Global Edition Chapter 22: Value at Risk and Expected Shortfall Multiple Choice Test Bank: Questions with Answers 1. Which of the following is true of the 99.9% value at risk?

A. There is 1 chance in 10 that the loss will be greater than the value of risk.

B. There is 1 chance in 100 that the loss will be greater than the value of risk.

C. There is 1 chance in 1000 that the loss will be greater than the value of risk.

D. None of the above.

Answer: C A 99.9% VaR means that there is a 0.1% chance of the loss exceeding the VaR level. This is 1 chance in 1000.

2. The gain from a project is equally likely to have any value between –$0.15 million and +$0.85 million. What is the 99% value at risk?

A. $0.145 million B. $0.14 million C. $0.13 million D. $0.10 million Answer: B The gain is uniformly distributed between −0.15 and +0.85 million dollars. The probability that it will be between −0.15 and −0.14 million dollars is therefore 1%. This means that there is a 99% chance that the loss will not be greater than $0.14 million. This is the 99% VaR. 3. The gain from a project is equally likely to have any value between −$0.15 million and +$0.85 million. What is the 99% expected shortfall?

A. $0.145 million B. $0.14 million C. $0.13 million D. $0.10 million Answer: A As explained in the answer to the previous question, the VaR level is $0.14 million.

Conditional on the loss being greater than $0.14 million, it is equally likely to have any value between $0.14 million and $0.15 million. The expected loss conditional that it is greater than $0.14 million is therefore $0.145 million. This is the expected shortfall.

4. Which of the following is true of the historical simulation method for calculating VaR? A. It fits historical data on the behavior of variables to a normal distribution.

B. It fits historical data on the behavior of variables to a lognormal distribution.

C. It assumes that what will happen in the future is a random sample from what has

happened in the past.

D. It uses Monte Carlo simulation to create random future scenarios.

Answer: C The historical simulation method assumes that the percentage changes in all market variables during the next day is a random sample from the percentage changes in a certain number of past days.

5. The 10-day VaR is often assumed to be which of the following?

A. The 1-day VaR multiplied by 10 B. The 1-day VaR multiplied by the square root of10 C. The 1-day VaR divided by 10 D. The 1-day VaR divided by the square root of 10 Answer: B The Basel committee rules allow the 10-VaR to be calculated as the one-day VaR multiplied by the square root of 10. This is exactly true when losses on successive days have independent normal distributions with mean zero.

6. Which was the minimum capital requirement for market risk in the 1996 BIS Amendment?

A. At least 3 times the 10-day VaR with a 99% confidence level B. At least 3 times 7-day VaR with a 97% confidence level C. At least 2 times 5-day VaR with a 95% confidence level D. 1-day VaR with a 99% confidence level Answer: A The 1996 amendment calculated capital as k times the 10-day 99% VaR where k was at least 3.

7. An investor has $2,000 invested in stock A and $5,000 in stock B. The daily volatilities of A and B are 1.5% and 1%, respectively, and the coefficient of correlation is 0.8. What is the one day 99% VaR? Assume that returns are multivariate normal (Note that N(–2.326) = 0.01) A. $177 B. $135 C. $215 D. $331 Answer: A The standard deviation of the change in the stock A position in one day is 2,000 × 0.015 = $30. The standard deviation of the change in the value of the stock B position in one day is 5,000 × 0.01 = $50. The variance of the combined position is

302 + 502 + 2 × 0.8 × 30 × 50 = 5,800. The standard deviation is the square root of this or 76.16 and the 99% VaR is therefore 2.326 times 76.16 this or about $177.

8. What is the method of testing how often a VaR with a certain confidence level was exceeded in the past called?

A. Stress testing B. Back testing C. EWMA D. The model-building approach Answer: B Back testing involves examining how well a particular VaR methodology would have worked in the past. It counts exceptions, which are situations where the VaR level that would have been calculated, was exceeded.

9. Which of the following is true when delta, but not gamma, is used in calculating VaR for option positions?

A. VaR for a long call is too low and VaR for a long put is too low.

B. VaR for a long call is too low and VaR for a long put is too high.

C. VaR for a long call is too high and VaR for a long put is too low.

D. VaR for a long call is too high and VaR for a long put is too high.

Answer: D When gamma is ignored, VaR for long option positions is too high and VaR for short option positions is too low. This is demonstrated for calls in Figures 22.5 and 22.6. The same can easily be seen to be true for puts.

10. Which of the following is true?

A. The quadratic model approximates daily changes using delta and gamma.

B. The quadratic model approximates daily changes using delta, but not gamma.

C. The quadratic model approximates daily changes using gamma, but not delta.

D. None of the above.

Answer: A The quadratic model uses delta and gamma to approximate daily changes as described in Section 22.5.

11. Which of the following is true?

A. Cash flow mapping is a way of calculating the present value of cash flows.

B. Cash flow mapping is used to handle interest rate exposures in the model building approach.

C. Cash flow mapping is used to handle interest rate exposures in the historical simulation approach.

D. None of the above.

Answer: B Cash flow mapping is a way to handle interest rates when the model building approach is used. (See page 506–507.)

12. Which of the following describes stressed VaR? A. It is based on movements in market variables in stressed market conditions.

B. It is VaR with a very high confidence level.

C. It is VaR multiplied by a factor of 3.

D. None of the above.

Answer: A Stressed VaR was introduced in Basel II.5. It calculates VaR based on movements in market variables in stressed market conditions.

13. A German bank has exposure to the S&P 500. Which of the following is true?

A. The S&P 500 index should be always be measured in U.S. dollars when VaR is calculated.

B. The S&P 500 index should be always be measured in euros when VaR is calculated.

C. Either A or B can be done.

D. The S&P 500 index should be measured in euros only if the bank has not got a U.S. subsidiary.

Answer: B All foreign assets should be measured in the domestic currency.

14. Which of the following is true of a covariance matrix?

A. The numbers on the diagonal are variances.

B. The numbers on the diagonal are standard deviations.

C. The numbers on the diagonal are all one.

D. The numbers on the diagonal are all zero.

Answer: A The diagonal numbers are variances. The off-diagonal numbers show the covariance between two variables.

15. Consider a position in options on a particular stock. The position has a delta of 12 and the stock price is 10. Which of the following is the approximate relation between the change in the portfolio value in one day, dP, and the return on the stock during the day, dx?

A. dP = 12dx B. dP = 1.2dx C. dP = 120dx D. dP = 22dx

Answer: C If S is the stock price and the change in the stock price is dS, from the definition of delta we know that dP = 12dS. This means that dP = 12S(dS/S). dS/S is dx. In this case, S = 10 so that C is correct.

16. A position in options on a particular stock has a delta of zero and a gamma of 4. The stock price is 10. Which of the following is the approximate relation between the change in the portfolio value in one day, dP, and the return on the stock, dx?

A. dP = 4 times the square of dx B. dP = 2 times the square of dx C. dP = 20 times the square of dx D. dP = 200 times the square of dx Answer: D If S is the stock price and the change in the stock price is dS, the change in the portfolio value is 0.5 × 4 × (dS)2. This is 2S2(dS/S)2. dS/S is dx. In this case S = 10 so that D is correct.

17. In a principal components analysis which of the following is the quantity of a particular factor in an observation?

A. Factor loading B. Factor score C. Factor size D. Factor rating Answer: B The quantity of a particular factor in the observation of changes on a particular day is known as the factor score.

18. In the case of interest rate movements, the most important factor corresponds to: A. A parallel shift B. A slope change C. A bowing D. An increase in short rates Answer: A The most important factor is the one corresponding to a parallel shift. This accounted for over 90% of the variance for the data in Section 22.9.

19. In the case of interest rate movements, the second most important factor corresponds to: A. A parallel shift B. A slope change

C. A bowing D. An increase in short rates Answer: B The second most important factor is a slope change (or twist). In the example in Section 22.9, this accounted for about 7% of the variance in the data.

20. Which of the following is true?

A. Expected shortfall is always less than VaR. B. Expected shortfall is always greater than VaR. C. Expected shortfall is sometimes greater than VaR and sometimes less than VaR. D. Expected shortfall is a measure of liquidity risk wheras VaR is a measure of market risk.

Answer: B Expected shortfall and VaR can both measure market risk. Expected shortfall is the expected loss level conditional on the loss level being greater than VaR. By definition expected shortfall must be greater than VaR.

Hull: Options, Futures, and Other Derivatives, Eleventh Edition, Global Edition Chapter 23: Estimating Volatilities and Correlations Multiple Choice Test Bank: Questions with Answers 1. How many parameters are necessary to define an EWMA model?

A. 1 B. 2 C. 3 D. 4 Answer: A One parameter (lambda) is necessary to define an EWMA model.

2. How many parameters are necessary to define a GARCH (1,1) model?

A. 1 B. 2 C. 3 D. 4 Answer: C Three parameters (omega, alpha, and beta) are necessary to define a GARCH (1,1) model.

3. At the end of Thursday, the estimated volatility of asset A is 2% per day. During Friday asset A produces a return of 3%. An EWMA model with lambda equal to 0.9 is used. What is an estimate of the volatility of asset A at the end of Friday?

A. 2.08% B. 2.10% C. 2.12% D. 2.14% Answer: C The variance rate is 0.9 × 0.022 + 0.1 × 0.032 = 0.00045. The volatility per day is the square root of this or 2.12%.

4. At the end of Thursday, the estimated volatility of asset B is 1% per day. During Friday asset B produces a return of zero. An EWMA model with lambda equal to 0.9 is used. What is an estimate of the volatility of asset B at the end of Friday?

A. 0.98% B. 0.95% C. 0.92% D. 0.90%

Answer: B The variance rate is 0.9 × 0.012 + 0.1 × 0.02 = 0.00009. The volatility per day is the square root of this or 0.95%.

5. At the end of Thursday, the estimated covariance between assets A and B is 0.0001. During Friday, asset A produces a return of 3% and asset B produces a return of zero. An EWMA model with lambda equal to 0.9 is used. What is an estimate of the covariance at the end of Friday?

A. 0.000090 B. 0.000081 C. 0.000100 D. 0.000095 Answer: A The covariance is 0.9 × 0.0001 + 0.1 × 0.03 × 0 = 0.000090.

6. Which of the following is a definition of the covariance between X and Y? A. Correlation between X and Y times variance of X times variance of Y. B. Variance of X times the variance of Y. C. Correlation between X and Y divided by the product of the standard deviation of X and the standard deviation of Y. D. Correlation between X and Y times standard deviation of X times standard deviation of Y. Answer: D Covariance is the coefficient of correlation multiplied by the product of the two standard deviations.

7. What does EWMA stand for?

A. Equally weighted moving average B. Equally weighted median approximation C. Exponentially weighted moving average D. Exponentially weighted median average Answer: C EWMA stands for exponentially weighted moving average.

8. Which of the following is true when the parameter lambda equals 0.95?

A. The weight given to the most recent observation is 0.95.

B. The weight given to the observation one day ago is 95% of the weight given to the observation two days ago.

C. The weights given to observations add up to 0.95.

D. The weights given to the observation two days ago is 95% of the weight given to the observation one day ago.

Answer: D The weights given to observations go down by 5% for each day we go back in time.

9. Which of the following is true of maximum likelihood methods?

A. They calculate the maximum possible values for parameters.

B. They calculate parameters that give the highest probability of past data occurring.

C. They calculate values for key variables that are most likely to occur in the future.

D. They involve a multivariate regression analysis.

Answer: B Maximum likelihood methods are concerned with estimating parameter values by searching for the values that maximize the chance of observed data occurring.

10. If the volatility for a portfolio is 20% per year, what is the volatility per quarter?

A. 20% B. 10% C. 5% D. 2% Answer: B The volatility per quarter is 0.2 ´ 0.25 = 0.1or 10%.

11. Which of the following is true?

A. GARCH models incorporate mean reversion; EWMA models do not.

B. EWMA models incorporate mean reversion; GARCH models do not.

C. Both GARCH and EWMA models incorporate mean reversion.

D. Neither GARCH nor EWMA models incorporate mean reversion.

Answer: A GARCH models incorporate mean reversion; EWMA models do not.

12. Which of the following is true?

A. All option implied volatilities tend to move by the same amount from one day to the next.

B. The implied volatilities of long-dated options tend to move by more than the implied volatilities of short-dated options.

C. The implied volatilities of short-dated options tend to move by more than the implied volatilities of long-dated options.

D. Sometimes B is true and sometimes C is true.

Answer: C When there is a shock causing an increase or decrease in volatility, its impact tends to disappear over time. (This is the effect of mean reversion.) The result is that the increase or decrease volatility has most effect on the implied volatilities of short-dated options.

13. Which of the following is true of a positive semi-definite variance-covariance matrix?

A. All elements of the matrix are positive.

B. The determinant of the matrix is positive.

C. The matrix has ones on the diagonal.

D. The matrix is internally consistent.

Answer: D The correlations between many different variables are not internally consistent unless the variance-covariance matrix is positive semi-definite.

14. Which of the following is true?

A. Volatilities and correlations decreased in the second half of 2008.

B. Volatilities and correlations increased in the second half of 2008.

C. Volatilities decreased and correlations increased in the second half of 2008.

D. Volatilities increased and correlations decreased in the second half of 2008.

Answer: B As the four-index example in the chapter shows, both volatilities and correlations increased in the second half of 2008.

15. The parameters in a GARCH (1,1) model are: omega = 0.000002, alpha = 0.04, and beta = 0.95.

The current estimate of the volatility level is 1% per day. If we observe a change in the value of the variable equal to 2%, how does the estimate of the volatility change?

A. 1.26% B. 1.16% C. 1.06% D. 1.03% Answer: C The new variance rate is 0.000002 + 0.04 × 0.022 + 0.95 × 0.012 = 0.000113. The new volatility is the square root of this or 1.06% 16. The parameters in a GARCH (1,1) model are: omega = 0.000002, alpha = 0.04, and beta = 0.95.

Which of the following is the closest to the long run average volatility?

A. 1.1% B. 1.2% C. 1.3% D. 1.4%

Answer: D The long run average variance rate is 0.000002/(1 − 0.04 − 0.95) = 0.0002. The long run average volatility per day is the square root of this or 1.4% 17. The parameters in a GARCH (1,1) model are: omega = 0.000002, alpha = 0.04, and beta = 0.95.

The current estimate of the volatility level is 1% per day. What is the expected volatility in 20 days?

A. 1.09% B. 1.10% C. 1.11% D. 1.12% Answer: A The long run average variance rate is 0.000002/(1−0.04−0.95) = 0.0002. The expected variance rate in 20 days is 0.0002 + (0.04 + 0.95)20× (0.012– 0.0002) = 0.000118. The volatility per day is the square root of this or 1.09%.

18. Which of the following is true?

A. GARCH (1,1) will always give a maximum likelihood at least as high as EWMA. B. EWMA will always give a maximum likelihood at least as high as GARCH (1,1).

C. The maximum likelihood is the same for GARCH (1,1) and EWMA. D. Sometimes A is true and sometimes B is true.

Answer: A EWMA is the particular case of GARCH (1,1) when the omega parameter is zero. It follows that GARCH (1,1) must give at least as good a fit to the data as EWMA. 19. The parameters in a GARCH (1,1) model are: omega = 0.000002, alpha = 0.04, and beta = 0.95.

What is the reversion rate for the variance rate implied by the model?

A. 0.5% per day B. 1.0% per day C. 1.5% per day D. 2.0% per day Answer: B The reversion rate is 1 − a - b. In this case, it is 1 − 0.04 − 0.95 = 0.01 or 1% per day.

20. Which of the following is true?

A. EWMA is a particular case of GARCH (1,1) where the reversion rate is zero.

B. EWMA has a lower reversion rate than GARCH (1,1), but it is not zero.

C. EWMA has a higher reversion rate than GARCH (1,1).

D. Sometimes EWMA has a higher reversion rate than GARCH (1,1) and sometimes it has a

lower reversion rate than GARCH (1,1).

Answer: A The reversion rate is 1 − a - b in GARCH (1,1). EWMA is a particular case of the GARCH (1,1) model where w = 0, and a + b = 1. This means that the reversion rate is zero.

Hull: Options, Futures, and Other Derivatives, Eleventh Edition, Global Edition Chapter 24: Credit Risk Multiple Choice Test Bank: Questions with Answers 1. Suppose that the cumulative probability of a company defaulting by years one, two, three and four are 3%, 6.5%, 10%, and 14.5%, respectively. What is the probability of default in the fourth year conditional on no earlier default?

A. 4.5% B. 5.0% C. 5.5% D. 6.0% Answer: B The unconditional PD for the fourth year is 14.5% minus 10% or 4.5%. The probability of no earlier default is 90%. The PD conditional on no earlier default is therefore 0.045/0.9 = 0.05 or 5% 2. Which of the following is usually used to define the recovery rate of a bond?

A. The value of the bond immediately after default as a percent of its face value.

B. The value of the bond immediately after default as a percent of the sum of the bond’s face value and accrued interest.

C. The amount finally realized by a bondholder as a percent of face value.

D. The amount finally realized by a bondholder as a percent of the sum of the bond’s face value and accrued interest.

Answer: A The recovery rate for a bond is usually defined as the value of the bond immediately after a default as a percent of its face value. This is in spite of the fact that the bond holder’s claim in the event of a default in many jurisdictions is the face value plus accrued interest.

3. Which of the following is true?

A. Risk neutral default probabilities are usually much lower than real world default probabilities.

B. Risk neutral default probabilities are usually much higher than real world default probabilities.

C. Risk neutral and real world probabilities must be close to each other if there are to be no arbitrage opportunities.

D. Risk-neutral default probabilities cannot be calculated from CDS spreads.

Answer: B Risk neutral default probabilities are usually greater than real world default probabilities.

4. A hazard rate is 1% per annum. What is the probability of a default during the first two years?

A. 2.00%

B. 2.02% C. 1.98% D. 1.96% Answer: C The probability of no default is e−0.01×2 = 0.9802. The probability of default is one minus this or 0.0198 (i.e., 1.98%).

5. Which of the following is true?

A. The default probability per year for a company always increases as we look further ahead.

B. The default probability per year for a company always decreases as we look further ahead.

C. Sometimes A is true and sometimes B is true.

D. The default probability per year is roughly constant for most companies.

Answer: C For investment grade companies, the probability of default tends to increase with time. For non-investment grade companies, the reverse is often true.

6. Which of the following is true?

A. Conditional default probabilities are at least as high as unconditional default probabilities.

B. Conditional default probabilities are at least as low as unconditional default probabilities.

C. Conditional default probabilities are sometimes lower and sometimes higher than unconditional default probabilities.

D. There is no difference between conditional and unconditional default probabilities because a company can only default once.

Answer: A The conditional default probability for a future time period is the unconditional default probability divided by the probability of no earlier default. The latter is less than or equal to one. As a result, the conditional probability is at least as great as the unconditional probability.

7. If a company’s five year credit spread is 200 basis points and the recovery rate in the event of a default is estimated to be 20%, what is the average hazard rate per year over the five years?

A. 0.4% B. 1.2% C. 1.8% D. 2.5% Answer: D

The average hazard rate is the credit spread divided by one minus the recovery rate. In this case, we get 0.02/0.8 = 0.025 or 2.5% 8. Which of the following is true?

A. Recovery rates are lower for investment grade companies.

B. Recovery rates are higher for non-investment grade companies.

C. Recovery rates are negatively correlated with default rates.

D. Recovery rates are positively correlated with default rates.

Answer: C When default rates are high in the economy, recovery rates tends to be low?

9. Which of the following is true?

A. The asset swap spread is a measure of excess of the bond yield over the OIS rate.

B. The asset swap spread is a measure of excess of the bond yield over the LIBOR/swap rate.

C. An asset swap exchanges the actual return on the asset for LIBOR plus a spread.

D. None of the above.

Answer: B The asset swap spread is a measure of the excess of the bond yield over LIBOR. In an asset swap, the promised cash flows (not the actual cash flows) on a bond are exchanged for LIBOR plus a spread.

10. To be investment grade, a company has to have a credit rating of: A. AA or better B. A or better C. BBB or better D. BB or better Answer: C Companies with credit ratings of BBB or better are investment grade.

11. In the Gaussian copula model, which of the following is true?

A. The time to default for a company is assumed to be normally distributed.

B. The time to default for a company is assumed to be lognormally distributed.

C. The time to default for a company is transformed to a normal distribution.

D. The time to default for a company is transformed to a lognormal distribution.

Answer: C The time to default for each company is transformed to a normal distribution on a percentile to percentile basis and the normal distributions are assumed to be multivariate normal.

12. Which of the following is true?

A. Netting always leads to a reduction in a company’s exposure to a counterparty.

B. Netting always leads to a company’s exposure to a counterparty either staying the same or going down.

C. Netting always increases a company’s exposure to a counterparty.

D. Netting can increase or reduce the exposure.

Answer: B Netting means that the derivatives portfolio with a counterparty is considered to be a single transaction in the event of a default. This cannot increase the exposure. If there are transactions in the portfolio with both positive and negative values, the exposure will go down.

13. Which of the following is true?

A. Downgrade triggers are particularly valuable if they are widely used by a company’s counterparties.

B. Downgrade triggers become less valuable if they are widely used by a company’s counterparties.

C. Downgrade triggers are useless because their impact is always anticipated by the market.

D. Downgrade triggers are a two-edged sword. If company A has a downgrade trigger for company B, then company B has a downgrade trigger for company A. Answer: B Downgrade triggers become less valuable if many of a company’s counterparties are using them (as was the case with Enron and AIG). This is because the counterparties will require either cash collateral, or transactions to be unwound, at the same time. This can cause the company to fail.

14. Which of the following is true of Merton’s model?

A. The equity is a call option on the assets.

B. The assets are a call option on the debt.

C. The debt is a call option on the equity.

D. The equity is a call option on the debt.

Answer: A In Merton’s model, the market value of the equity of a company is a call option on the market value of the assets.

15. Which of the following is true of Merton’s model?

A. The strike price is the market value of the debt.

B. The strike price is the market value of the equity.

C. The strike price is the book value of the equity.

D. The strike price is the face value of the debt.

Answer: D In Merton’s model, the strike price is the face value of the debt.

16. Which of the following is true?

A. The Gaussian copula model assumes that the defaults of different companies are independent.

B. The Gaussian copula model assumes that defaults, conditional on the value of a factor, are independent.

C. The Gaussian copula model assumes that the number of defaults is normally distributed.

D. None of the above.

Answer: B The Gaussian copula model is analyzed by noting that defaults conditional on a factor are independent.

17. A derivatives dealer has a single transaction with a company which is a long position in a fiveyear option. The Black–Scholes–Merton value of the option is $6. Suppose that the credit spread on five-year bonds issued by the company is 100 basis points. What is the dealer’s CVA per option purchased from the counterparty?

A. $0.19 B. $1.19 C. $0.29 D. $1.29 Answer: C The value of the option when the counterparty’s credit risk is taken into account is 6e−0.01×5 = 5.71 and so the CVA is 6 − 5.71 or $0.29 per option purchased.

18.

Which of the following is true?

A. A derivative dealer’s CVA is the counterparty’s DVA and vice versa.

B. Collateral posted by the counterparty reduces CVA. C. Collateral posted by the dealer reduces DVA. D. All of the above.

Answer: D A, B, and C are all true.

19.

The credit spreads for a counterparty for 5 and 6 years are 2% and 2.2%, respectively. The recovery rate is 60%. What is closest to the unconditional default probability for the sixth year?

A. 0.04 B. 0.05 C. 0.06 D. 0.07

Answer: C The average hazard rate for the first five years is 0.02/(1 – 0.6) = 0.05 or 5%. The average hazard rate for the first six years is 0.022/(1 – 0.6) = 0.055 or 5.5%. The probability of no default during the first five years is therefore e-0.05×5 = 0.7788. The probability of no default during the first six years is e-0.055×6 = 0.7189. The probability of default during the sixth year is therefore 0.7788 − 0.7189 or approximately 0.06.

20.

Which of the following is true of Creditmetrics when it is used to calculate credit VaR? A. Creditmetrics takes defaults but not downgrades into account.

B. Creditmetrics takes downgrades but not defaults into account.

C. Creditmetrics considers neither defaults nor downgrades.

D. Creditmetrics considers both defaults and downgrades.

Answer: D By working from the credit transition matrix, Creditmetrics takes both downgrades and defaults into account.

Hull: Options, Futures, and Other Derivatives, Eleventh Edition, Global Edition Chapter 25: Credit Derivatives Multiple Choice Test Bank: Questions with Answers

1. What is the number of companies underlying the CDX NA IG index?

A. 50 B. 75 C. 100 D. 125 Answer: D There are 125 investment grade companies underlying CDX NA IG. 2. What is the number of companies underlying the iTraxx index?

A. 50 B. 75 C. 100 D. 125 Answer: D There are 125 investment grade companies underlying iTraxx.

3. What is the rating of the companies underlying the iTraxx index?

A. A or above B. BBB or above C. BB or below D. BBB or below Answer: B The companies underlying iTraxx must be investment grade. This means that their credit ratings must be BBB or above.

4. In a CDS with a notional principal of $100 million the reference entity defaults. What is the payoff to the buyer of protection when the recovery rate is 30%?

A. $100 million B. $30 million C. $130 million D. $70 million Answer: D The payoff is the notional principal times one minus the recovery. In this case, this is 100 × (1 − 0.3) or $70 million.

5. In a one-year forward contract on a CDS that will last five years, what usually happens if there is a default during the first year?

A. There is a payoff to the forward protection buyer at the time of default.

B. There is a payoff to the forward protection buyer at the end of one year.

C. There is a payoff to the forward protection buyer at the end of six years.

D. The contract ceases to exist.

Answer: D A forward CDS contract ceases to exist if there is a default before the maturity of the forward contract.

6. Which of the following happens when the default correlation of the companies underlying a CDO increases?

A. The value of the senior tranche and the equity tranche to the protection buyer both increase.

B. The value of the senior tranche and the equity tranche to the protection buyer both decrease.

C. The value of the senior tranche to the protection buyer decreases and the value of the equity tranche to the protection buyer increases.

D. The value of the senior tranche to the protection buyer increases and the value of the equity tranche to the protection buyer decreases.

Answer: D Senior tranches are more likely to experience losses and so their value to the protection buyer increases. The equity tranche is less likely to experience losses and so its value to the protection buyer decreases. (The total expected loss of all tranches stays the same.) This answer is best understood by thinking about the situation where every company has a 2% probability of defaulting. What is the situation if the correlation is zero? What is the situation when the correlation is perfect?

7. Which of the following is true of a synthetic CDO? A. It is created from portfolios of bonds.

B. It is created from portfolios of CDSs. C. It references a standard portfolio of bonds.

D. None of the above.

Answer: B A synthetic CDO is created from a portfolio of CDSs where protection has been sold on each name.

8. A CDS with a number of reference entities provides for each reference entity a payoff if it defaults. What is a name for this CDS? A. Binary CDS B. Add-up Basket CDS

C. First-to-Default CDS D. n-to-Default CDS Answer: B This is a portfolio of CDSs and is known as an add-up basket.

9. Which of the following is the most popular life for a credit default swap?

A. 1 year B. 3 years C. 5 years D. 10 years Answer: C 5 years is the most popular life for a CDS. 10. If the CDS spread for a regular 5-year CDS is 120 basis points, what is the CDS spread for a 5-year binary CDS on the same underlying reference entity? Assume a recovery rate of 40%.

A. 48 basis points B. 72 basis points C. 200 basis points D. 300 basis points Answer: C The payoff from a regular CDS is (1 − R) times the payoff from a binary CDS where R is the recovery rate. It follows that the CDS for a binary CDS is 120/(1 − 0.4) or 200 basis points.

11. For what range of losses is the equity tranche of iTraxx (or CDX NA IG) responsible?

A. 0 to 10% B. 0 to 7% C. 0 to 6% D. 0 to 3% Answer: D The equity tranche covers losses between 0 and 3% of the total principal.

12. Which of the following is true about a CDS? A. Restructuring is never a credit event.

B. Restructuring is always a credit event.

C. Certain types of restructuring qualify as credit events but others do not.

D. Sometimes a CDS is defined so that restructuring is a credit event and sometimes it is not.

Answer: D Sometimes restructuring is included as a credit event and sometimes it is not.

13. If the CDS-bond basis is X minus Y, what are X and Y? A. X is the CDS spread and Y is the excess of the bond yield over the swap rate.

B. X is the excess of the bond yield over the swap rate and Y is the CDS spread.

C. X is the CDS spread and Y is the excess of the bond yield over the Treasury rate.

D. X is the excess of the bond yield over the Treasury rate and Y is the CDS spread.

Answer: A The CDS-bond basis is the excess of the CDS spread over the bond yield spread.

14. In the Lehman bankruptcy, the payoff to people who had bought CDS protection was 91.375% of the notional principal. How was this determined?

A. By calculation of the cheapest-to-deliver bond B. By an auction process C. By a calculation agent D. By Lehman’s liquidators Answer: B An auction process is now used to determine cash payoffs on CDSs in the event of a default.

15. Which of the following best describes a total return swap?

A. It exchanges the realized return on an asset, including both income and capital gains/losses, for a return, equal to LIBOR plus a spread on the initial value of the asset.

B. It exchanges the promised return on an asset, including both income and capital gains/losses, for a return equal to LIBOR plus a spread on the initial value of the asset.

C. It exchanges the realized return on an asset, including income but not capital gains/losses, for a return equal to LIBOR plus a spread on the initial value of the asset.

D. It exchanges the promised return on an asset, including income but not capital gains/losses, for a return equal to LIBOR plus a spread on the initial value of the asset.

Answer: A A total return swap exchanges the actual (not the promised) return on an asset for LIBOR plus a spread.

16. If a tranche spread is 55 basis points and the fixed coupon is 60 basis points, which of the following happens when a trader buys protection?

A. The trader pays an estimate of the present value of 5 basis points per year and then pays 55 basis points per year.

B. The trader pays an estimate of the present value of 5 basis points per year and then pays 60 basis points per year.

C. The trader receives an estimate of the present value of 5 basis points per year and then pays 55 basis points per year.

D. The trader receives an estimate of the present value of 5 basis points per year and then pays 60 basis points per year.

Answer: D Trading is organized so that the trader pays 60 basis points. Because the spread is actually only 55 basis points, the trader receives an estimate of the present value of 5 basis points per year at the outset. This means that the tranche trades like a bond.

17. A portfolio of ten companies is formed. In a third-to-default swap (circle one): A. There is a payoff when the third default on the portfolio happens.

B. There is a payoff when the first, second and third companies defaults happen.

C. There is a payoff when the third, fourth, fifth…tenth companies defaults happen.

D. None of the above.

Answer: A There is a payoff when the third default happens.

18. The yield on a company’s five-year bonds is 5%. The five-year swap rate is 4.5% and the five-year Treasury rate is 4%. What would be closest to your best estimate of the five-year CDS spread?

A. 200 basis points B. 150 basis points C. 100 basis points D. 50 basis points Answer: D The best estimate is the excess of the bond yield over the swap rate or about 50 basis points.

19. Gaussian quadrature is: A. A quadratic spline approximation to a normal distribution.

B. A way to approximate an integral of a function of a normally distribute variable as a sum of terms.

C. A procedure for speeding up Monte Carlo simulation when credit derivatives are valued.

D. An alternative to a look up table to determining values of the cumulative normal distribution.

Answer: B Gaussian quadrature is a way of integrating over a normally distributed factor when CDOs are valued using the Gaussian copula model. Extreme values of the factor are considered appropriately.

20. Which of the following describes “base correlation”?

A. The most basic correlation measure possible.

B. A correlation used to value all tranches.

C. The correlation implied from market data.

D. The correlation for valuing a tranche with an attachment point of 0%.

Answer: D The base correlation for X% is the correlation that would be used to value a tranche which provides protection against the first X% of losses on a portfolio. The tranche considered has an attachment point of 0% and a detachment point of X%.

Hull: Options, Futures, and Other Derivatives, Eleventh Edition, Global Edition Chapter 26: Exotic Options Multiple Choice Test Bank: Questions with Answers

1. An Asian option is a term used to describe which of the following?

A. An option where the payoff depends on whether a barrier is hit.

B. An option where the payoff depends on the average value of a variable over a period of time.

C. An option that trades on an exchange in the Far East.

D. Any option with a nonstandard payoff.

Answer: B An Asian option is an option whose payoff is calculated from the average value of a variable over a period of time.

2. As the barrier is observed more frequently, which of the following is true of a knock-out option?

A. It becomes more valuable.

B. It becomes less valuable.

C. There is no effect on value.

D. It may become more valuable or less valuable.

Answer: B As the barrier is observed more frequently, it is more likely to be hit. A knock-out option therefore becomes less valuable.

3. There are two types of regular options (calls and puts). How many types of compound options are there?

A. Two B. Four C. Six D. Eight Answer: B There are four: call on call, call on put, put on call, and put on put.

4. There are two types of regular options (calls and puts). How many types of barrier options are there?

A. Two B. Four C. Six D. Eight Answer: D

There are eight: up and in call, up and in put, down and in call, down and in put, up and out call, up and out put, down and out call, and down and out put.

5. In a shout call option, the strike price is $30. The holder shouts when the asset price is $40.

What is the payoff from the option if the final asset price is $35?

A. $0 B. $5 C. $10 D. $15 Answer: C The holder gets the intrinsic value at the time of the shout or the usual final payoff whichever is greater. In this case, the holder gets 40 − 30 = $10 6. A floating lookback call option pays off which of the following?

A. The amount by which the final stock price exceeds the minimum stock price.

B. The amount by which the maximum stock price exceeds the final stock price.

C. The amount by which the strike price exceeds the minimum stock price.

D. The amount by which the maximum stock price exceeds the strike price.

Answer: B A floating lookback call pays off the amount by which the maximum stock price exceeds the final stock price.

7. A fixed lookback put option pays off which of the following?

A. The amount by which the final stock price exceeds the minimum stock price.

B. The amount by which the maximum stock price exceeds the final stock price.

C. The amount by which the strike price exceeds the minimum stock price.

D. The amount by which the maximum stock price exceeds the strike price.

Answer: C A fixed lookback put pays off the amount by which the strike price exceeds the minimum stock price, if this is positive.

8. Which of the following is equivalent to a long position in a European call option?

A. A short position in a cash-or-nothing put option plus a long position in an asset-ornothing put option.

B. A long position in an asset-or-nothing put option plus a long position in a cash-ornothing put option.

C. A long position in an asset-or-nothing call option plus a long position in a cash-ornothing call option.

D. A long position in an asset-or-nothing call option plus a short position in a cash-ornothing call option.

Answer: D A long position in a European call is equivalent to a long position in an asset-or-nothing call option (this is worth S0N(d1)) and a short position in a cash-or-nothing call option (this is worth –Ke-rTN(d2))

9. Which of the following is equivalent to a short position in a European put option?

A. A short position in a cash-or-nothing put option plus a long position in an asset-ornothing put option.

B. A long position in an asset-or-nothing put option plus a long position in a cash-ornothing put option.

C. A long position in an asset-or-nothing call option plus a long position in a cash-ornothing call option.

D. A long position in an asset-or-nothing call option plus a short position in a cash-ornothing call option.

Answer: A A short position in a European put is equivalent to a short cash-or-nothing put option (−KN(−d2)e-rT) and a long position in an asset-or-nothing put (S0N(−d1)).

10. Which of the following describes a cliquet option?

A. An option to exchange one asset for another.

B. An instrument when the holder can choose between several alternative options.

C. An option on an option with predetermined strike prices for the two options.

D. A series of options with rules for determining strike prices.

Answer: D A cliquet option is a series of options where there are rules for determining strike prices. For example, there could be a series of one-year options where the strike price for each option is the asset price at the beginning of its life.

11. An employer has promised that it will grant employees three-year options in one year’s time and that the options will be at the money at the time they are granted. What describes these options?

A. Chooser options B. Forward start options C. Compound options D. Shout options Answer: B

These are referred to as forward start options because they are options that are certain to start at a particular future time.

12. When can Bermudan options be exercised?

A. Any time during the life of the options.

B. Any time after a certain date up to the end of the option’s life.

C. Any time before a certain date or at the end of the option’s life.

D. On dates specified at the start of the option.

Answer: D Bermudan options can be exercised on specified dates but not all dates. (Bermuda is between Europe and America!).

13. Which of the following is the payoff from an average strike call option?

A. The excess of the strike price over the average stock price, if positive.

B. The excess of the final stock price over the average stock price, if positive.

C. The excess of the average stock price over the strike price, if positive.

D. The excess of the average stock price over the final stock price, if positive.

Answer: B An average strike call pays off the excess of the final stock price over the average stock price if this is positive.

14. Which of the following is the payoff from an average strike put option?

A. The excess of the strike price over the average stock price, if positive.

B. The excess of the final stock price over the average stock price, if positive.

C. The excess of the average stock price over the strike price, if positive.

D. The excess of the average stock price over the final stock price, if positive.

Answer: D An average strike put pays off the excess of the average stock price over the final stock price if this is positive.

15. A binary option pays off $100 if a non-dividend-paying stock price is greater than its current value in three months. The risk-free rate is 3% and the volatility is 40%. Which of the following is its value?

A. 99.25N(−0.1375) B. 99.25N(0.1375) C. 99.25N(−0.0625) D. 99.25N(0.0625) Answer: C

The binary call option is worth 100N(d2)e-0.03×0.25. In this case, S0 = K so than ln(S0/K) = 1 and

d2 =

(0.03 - 0.42 / 2) ´ 0.25 = -0.0625 0.4 ´ 0.25

16. A volatility swap is: A. An instrument that swaps the change in the value of a market variable for a fixed amount.

B. A swap involving an asset whose volatility is greater than a certain level.

C. An exchange of the implied volatility of an option at a future time for a fixed volatility.

D. An exchange of the realized volatility of an asset for a fixed volatility.

Answer: D A volatility swap is an exchange of the realized volatility of an asset over a period of time for a prespecified fixed volatility with both being multiplied by a notional principal.

17. Which of the following is true of a gap option?

A. The strike price determining whether a payoff is made is not the same as the strike price determining the size of the payoff.

B. There is a straightforward valuation formula similar to Black−Scholes−Merton.

C. It describes an option where there is a cost to exercising.

D. All of the above.

Answer: D All of A, B, and C are true. A gap call option provides a payoff of ST – K1 when ST > K2. A gap put option provides a payoff of K1-ST when ST < K2 18. Which of the following is true?

A. A variance swap is worth the square of a volatility swap.

B. The payments on a variance swap are the square of the payments on a volatility swap.

C. Variance swaps can be valued in terms of European call and put options.

D. None of the above.

Answer: C Variance swaps can be valued in terms of European put and call options.

19. Static options replication for a portfolio of American options on a stock involves: A. Finding a hedge portfolio to match daily changes.

B. Finding a hedge portfolio to match values on a boundary that is certain to be reached.

C. Finding a hedge portfolio to match values at one particular time.

D. Constructing a hedge taking both gamma and delta into account.

Answer: B

Static option replication involves finding a hedge portfolio that matches values on some boundary in {S,t} space that is certain to be crossed eventually. Once the boundary is reached, the hedge must be unwound and a new hedge created.

20. Exotic options: A. Can always be hedged just as easily as regular options.

B. Are easier to hedge than regular options.

C. Are more difficult to hedge than regular options.

D. Are sometimes easier and sometimes more difficult to hedge than regular options.

Answer: D Average price options are usually easier to hedge than regular options because as time passes there is progressively less uncertainty about what the final average will be. Barrier options are more difficult to hedge because of discontinuities.