Applied Derivatives
Exam Materials
Course Introduction
Applied Derivatives explores the practical aspects of financial derivatives, including options, futures, forwards, and swaps. The course covers the fundamental concepts of derivative pricing, risk management, and hedging strategies, emphasizing their applications in real-world financial markets. Through case studies and quantitative analysis, students learn how to design, value, and utilize derivative instruments to manage financial risk, optimize investment portfolios, and enhance decision-making in both corporate and investment banking settings.
Recommended Textbook
Derivatives Markets 3rd Edition by Robert L. McDonald
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2
Chapter 1: Introduction to Derivatives
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Q1) Which of the following is not a derivative instrument?
A) Contract to sell corn
B) Option agreement to buy land
C) Installment sales agreement
D) Mortgage backed security
Answer: C
Q2) Assume that an investor lends 100 shares of Jiffy,Inc.common stock to a short seller.The bid-ask prices are $32.00 - $32.50.When the position is closed,the bid-ask prices are $32.50 - $33.00.The commission rate is 0.5%.The market interest rate is 5.0% and the short rebate rate is 3.0%.Calculate the gain or loss to the lender.Assume the lender is not subject to a bid-ask loss or commissions.
A) $164.00 gain
B) $164.00 loss
C) $100.00 gain
D) $100.00 loss
Answer: A
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Chapter 2: An Introduction to Forwards and Options
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Q1) A put option is purchased and held for 1 year.The Exercise price on the underlying asset is $40.If the current price of the asset is $36.45 and the future value of the original option premium is (-$1.62),what is the put profit,if any,at the end of the year?
A) $1.62
B) $1.93
C) $3.55
D) $5.17
Answer: B
Q2) The spot price of the market index is $900.After 3 months the market index is priced at $920.The annual rate of interest on treasuries is 2.4% (0.2% per month).The premium on the long put,with an exercise price of $930,is $8.00.What is the profit or loss at expiration for the long put?
A) $2.00 gain
B) $2.00 loss
C) $1.95 gain
D) $1.95 loss
Answer: C
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Chapter 3: Insurance, collars, and Other Strategies
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Sample Questions
Q1) What is the difference between naked and covered call writing?
Answer: A covered position is one in which the individual also owns the underlying asset in addition to the short call.A naked position involves writing the call alone.
Q2) Why is a straddle position considered a speculation on the asset's volatility?
Answer: The strategy loses money if prices stay constant,but benefits from large changes in prices,either up or down.
Q3) A strategy consists of buying a market index product at $830 and longing a put on the index with a strike of $830.If the put premium is $18.00 and interest rates are 0.5% per month,what is the profit or loss at expiration (in 6 months)if the market index is $810?
A) $20.00 gain
B) $18.65 gain
C) $36.29 loss
D) $43.76 loss
Answer: D
Q4) Why might the manager of a portfolio employ a protective put strategy?
Answer: If the manager desires to protect against a price decline,but is restricted from selling assets,a long put creates a floor below which losses cannot occur.
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Chapter 4: Introduction to Risk Management
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Q1) A farmer sells 4 million bushels of corn at a spot price of $2.10 per bushel.The total cost of production was $9.2 million.The farmer has an effective tax rate of 25%.If the farmer entered into a futures contract at a price of $2.40 per bushel on 4 million bushels,what is the farmer's net loss or gain?
A) $100,000 loss
B) $800,000 loss
C) $300,000 gain
D) $400,000 gain
Q2) When selecting among various put options with different strike prices,in order to hedge a long asset position,which of the following statements is true?
A) Higher strike puts cost more and provide higher floors
B) Higher strike puts cost less and provide higher floors
C) Lower strike puts cost more and provide higher floors
D) Lower strike puts cost less and provide higher floors
Q3) Why are synthetics created and/or calculated when the actual derivative is available?
Q4) Why would a manufacturer elect to use a long call strategy instead of a forward contract to hedge the risk associated with variable costs?
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Page 6
Chapter 5: Financial Forwards and Futures
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Q1) Interest rates on the U.S.dollar are 5.4% and euro rates are 4.6%.Given a dollar per euro spot rate of 0.918,what is the 6-month forward rate ($/E)?
A) 0.912
B) 0.917
C) 0.922
D) 0.934
Q2) Which of the following statements does NOT accurately reflect the relationship between securities and synthetic forward contracts?
A) Forward = stock - zero coupon bond
B) Zero coupon bond = stock - forward
C) Prepaid forward = forward - zero coupon bond
D) Stock = forward + zero coupon bond
Q3) What are some uses for index futures contracts?
Q4) Explain the steps necessary to take advantage of an arbitrage opportunity,which may exist between the dollar and yen,when a future yen payment is required.
Q5) Explain the impact transaction costs have on the ability to make arbitrage profits in forward and futures markets.
Q6) Name some advantages that futures contracts have over forward contracts.
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Chapter 6: Commodity Forwards and Futures
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Q1) The spot price of corn is $5.82 per bushel.The opportunity cost of capital for an investor is 0.6% per month.If storage costs of $0.03 per bushel per month are factored in,all else being equal,what is the future value of storage costs over a 6-month period?
A) $0.1534
B) $0.1684
C) $0.1772
D) $0.1827
Q2) Give one example of how price discovery functions in the commodity futures market.
Q3) Refer to the table 6.1.The lease rate on the 6-month soybean contract is 0.35%.What is the implied annual storage cost if the cost is continuously paid and proportional?
A) 0.84%
B) 1.62%
C) 2.30%
D) 4.0%
Q4) Explain how a negative correlation between agricultural production and commodity prices creates a natural hedge.
Q5) When is it possible for the lease rate to fall below zero?
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Page 8
Chapter 7: Interest Rate Forwards and Futures
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Q1) The price of a 3-year zero coupon government bond is 85.16.The price of a similar 4-year bond is 79.81.What is the yield to maturity (effective annual yield)on the 4-year bond?
A) 4.6%
B) 5.5%
C) 5.8%
D) 6.7%
Q2) Explain the process of creating a synthetic Forward Rate Agreement.
Q3) The prices of 1,2,3,and 4-year zero coupon government bonds are 95.42,90.36,85.16,and 78.81,respectively.What is the implied 2-year forward rate between years 2 and 4?
A) 4.8%
B) 5.2%
C) 5.5%
D) 6.4%
Q4) How is duration calculated? What is the nature and use of duration? How does duration compare to the linear concept of the bond price and interest rate relationship? Is duration better than convexity or worse? Duration is considered common knowledge in the fixed income world and should be discussed at length.
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Chapter 8: Swaps
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Q1) Assume oat forward prices over the next 3 years are $2.25,$2.35,and $2.28,respectively.Effective annual interest rates over the same period are 5.2%,5.5%,and 5.8%.What is the ?2-year swap price on a hypothetical "forward swap" that begins at the end of year 1?
A) $2.14
B) $2.32
C) $2.41
D) $2.53
Q2) Why do arbitrage profits rarely exist in interest rate swap pricing?
Q3) How does the existence of swaptions add to the possibilities in risk management techniques? While option strategies have not yet been discussed,students should be able to draw conclusions from prior chapters.Lead the class in a discussion of how options lead to an infinite range of possible strategies for swap investors.
Q4) How would a market-maker hedge a swap involving variable price and quantity?
Q5) Explain a "diff swap" as it relates to currency swaps.
Q6) Under what circumstances would a multinational company elect to enter into a currency swap agreement?
Q7) Describe briefly the nature of a swap and its primary component.
Page 10
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Chapter 9: Parity and Other Option Relationships
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Sample Questions
Q1) Jafee Corp.common stock is priced at $36.50 per share.The company just paid its $0.50 quarterly dividend.Interest rates are 6.0%.A $35.00 strike European call,maturing in 6 months,sells for $3.20.What is the price of a 6-month,$35.00 strike put option?
A) $1.20
B) $1.64
C) $2.04
D) $2.38
Q2) Explain in simple terms why a call option on a non-dividend paying stock should never be exercised early.
Q3) Call options with strikes of $30,$35,and $40 have option premiums of $1.50,$1.70,and $2.00,respectively.Using strike price convexity,which option premium,if any,is not possible?
A) C (30)
B) C (35)
C) C (40)
D) All are possible
Q4) Using the synthetic long stock strategy,explain the difference in call and put prices.
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11
Chapter 10: Binomial Option Pricing: Basic Concepts
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Sample Questions
Q1) Using a binomial tree explanation,explain the situation in which an American option would alter the pricing of an option.
Q2) Using a binomial tree,what is the price of a $40 strike 6-month call option,using 3-month intervals as the time period? Assume the following data: S = $37.90,r = 5.0%, = 0.35
A) $2.50
B) $2.76
C) $2.92
D) $3.08
Q3) The stock price in KMW,Inc.is $50,$54,$56,and $48 on four consecutive days of trading.What is the continuously compounded return on the stock over this time frame?
A) -3.85 %
B) -4.00 %
C) -4.08 %
D) -4.16 %
Q4) Draw the binomial tree listing only the option prices at each node.Assume the following data on a 6-month put option,using 3-month intervals as the time period.K = $40.00,S = $37.90,r = 5.0%, = 0.35
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Page 12
Chapter 11: Binomial Option Pricing: Selected Topics
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Sample Questions
Q1) A stock price is $85.00.Assume r = 0.07 and there is no dividend.What is the 6-month forward price?
A) $88.03
B) $89.16
C) $90.26
D) $92.33
Q2) Consider a two-period binomial model,where each period is 6 months.Assume the stock price is $50.00, = 0.20,r = 0.06 and the dividend yield = 3.5%.What is the lowest strike price where early exercise would occur with an American put option?
A) $50
B) $55
C) $60
D) $65
Q3) Under what circumstances should an option be exercised early?
Q4) What is the relationship between dividends and the forecasted stock price in a binomial model?
Q5) When developing a binomial tree model where stocks pay discrete dividends,what problem may occur?
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Chapter 12: The Black-Scholes Formula
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Sample Questions
Q1) Draw a payoff diagram for a long put position,depicting options that expire at 0,30 and 60 days.
Q2) Assume that a $75 strike call has a 1.0% continuous dividend,90 days until expiration and stock price of $72.00.What is the rho of the option as the interest rate changes from 6.0% to 5.0%?
A) 0.07
B) 0.12
C) 0.16
D) 0.20
Q3) Assume that a $55 strike call has a 1.5% continuous dividend,r = 0.05 and the stock price is $50.00.If the option has 45 days until expiration,what is the vega,given a shift in volatility from 33.0% to 34.0%?
A) 0.20
B) 0.15
C) 0.10
D) 0.05
Q4) What unique feature about perpetual options makes it possible to derive a valuation formula?
Q5) Which Greek is also called time decay and why?
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Chapter 13: Market-Making and Delta-Hedging
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Sample Questions
Q1) What actions are required to both delta-hedge and gamma-hedge a written option position?
Q2) What is net dollar gain or cost required to create a short put delta hedge against a 100 short put position? Assume puts are priced at $1.98,the delta is 0.489,the stock price is $34.50,and no cost to short stock.
A) $1,540.50 gain
B) $1,540.50 cost
C) $2,319.58 gain
D) $2,319.58 cost
Q3) Which of the following is NOT a source of cash while maintaining a delta neutral hedge?
A) Borrowing
B) Purchase or sale of shares
C) Interest
D) Self financing
Q4) What prevents a market-maker from readjusting her delta hedge on a continual basis?
Q5) Describe the true relationship between option prices and delta.Use calls as an example.
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Chapter 14: Exotic Options: I
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Q1) Assume S = $55,K = $55,r = 0.07, = 0.27,div = 0.0,and 180 days until expiration.What is the premium on an Asian average price call,where N = 5?
A) $2.89
B) $2.99
C) $3.09
D) $3.19
Q2) Assume S = $63,K = 60,div = 0,r = 0.04, = 0.35,and 90 days until expiration.What is the premium on a knock-in call option with an up-and-in barrier of $65?
A) $1.96
B) $2.06
C) $2.16
D) $2.26
Q3) The value of an Asian put option is computed using the geometric average strike.What is the expected payoff if the observed prices to date are 71,72,70,68,69,and 68,respectively?
A) 1.35
B) 1.45
C) 1.55
D) 1.65
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Page 16
Chapter 15: Financial Engineering and Security Design
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Q1) Dawn,Inc.stock is $37.00 per share.The company's semi-annual dividend is forecasted as $0.25 per share,increasing every 6 months by 20.0%.What is the price of a zero-coupon equity-linked bond,promising to pay one share in 4 years,given annual interest rates of 6.0%?
A) $32.29
B) $33.49
C) $34.39
D) $35.69
Q2) We wish to cap participation in a 3-year equity-linked option at 50.0% return.Our profit alpha is 3.0%.The S&P 500 price = 950,div = 0.015, = 0.22,and interest rates are 4.8%.What is the implied participation rate?
A) 0.66
B) 0.76
C) 0.96
D) 1.16
Q3) Instead of issuing a pure commodity-linked debt,why would the commodity producing firm consider a combining interest plus participation in the commodity price appreciation?
Q4) What possible tax advantage exists in equity-linked notes?
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Chapter 16: Corporate Applications
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Q1) Compute the yield on debt given a 10-year zero-coupon bond paying $500 at maturity.Assume the asset value is $450, = 0.35,r = 0.06,and no dividend is paid.
A) 6.62%
B) 7.26%
C) 8.26%
D) 9.62%
Q2) A company issues an option grant with an outperformance feature,against the S&P 500.Assume S&P 500 = 1100,S = 46,k = 45, = 0.30,r = 0.04,and 10 years until expiration.The S&P 500 has a dividend yield of 2.5%,standard deviation of 20.0% and a 0.45 correlation coefficient with the stock.What is the value of the outperformance feature?
A) $2.25
B) $3.29
C) $4.11
D) $4.78
Q3) The use of collars in acquisitions serves the purpose of addressing what two issues in an offer?
Q4) What three components exist in the value of an "outperform stock option"?
Q5) Why does a company sell a put when issuing compensation options?
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Chapter 17: Real Options
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Q1) An existing well is operating and the price of oil is $115 per barrel.The effective lease rate and risk free rate are 3.0% and 4.0%,respectively.The constant cost of extraction is $85 per barrel and the volatility of prices is 15.0%.If it costs nothing to shut down the well,at what price would we close the well?
A) $41
B) $48
C) $52
D) $59
Q2) Mead,Inc.may invest $20 million in a new fiber optic project.Due to market conditions,annual production costs and revenues are forecasted at $10 million and $8 million,respectively,starting next year.Revenues are expected to grow at 4.0% and interest rates are 6.0%.What is the change in value if the project is commenced in 5 years instead of today? (Use static analysis.)
A) $8.84 million
B) $10.84 million
C) $12.84 million
D) $14.84 million
Q3) What is the main difference in pricing R & D options versus most other real options?
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Chapter 18: The Lognormal Distribution
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Q1) What is the probability that a number drawn from the standard normal distribution will be between -0.60 and 0.45?
A) 0.40
B) 0.50
C) 0.60
D) 0.70
Q2) What is the area under the standard normal distribution curve and is less than 0.654?
A) 0.5115
B) 0.6215
C) 0.7434
D) 0.8283
Q3) What is the probability that a number drawn from the standard normal distribution will NOT be between -1 and 1?
A) 0.22
B) 0.32
C) 0.42
D) 0.52
Q4) Give a very brief definition of conditional expected stock price.
Q5) How are partial expectation prices converted to conditional expectation prices?
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Chapter 19: Monte Carlo Valuation
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Q1) Which of the following options would not benefit from using a Monte Carlo simulation?
A) American
B) Asian
C) European
D) Barrier
Q2) When a stock price movement occurs and is more than we would expect from a lognormal distribution,we refer to this as:
A) Pull
B) Jump
C) Squat
D) Push
Q3) What advantage does a variance reduction technique offer?
Q4) In what option does it benefit to simulate the path of potential asset prices?
A) Barrier
B) European
C) Asian
D) A and C
Q5) Why does an Asian option benefit from a larger number of draws in a Monte Carlo simulation?
21
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Chapter 20: Brownian Motion and Itos Lemma
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Q1) Assume a stock price of S(0)= $62.00,r = 0.05, = 0.30,and dividend = 0.What is the price of a claim that pays \( \sqrt{S} \) ? Use formula 20.29.
A) $7.59
B) $8.59
C) $9.59
D) $10.59
Q2) What are two important implications of assuming that prices follow a geometric Brownian motion?
Q3) For purposes of option pricing,when the movement of a stock price follows a geometric Brownian motion,the stock price is said to follow which type of distribution?
A) Bimodal
B) Latin hypercube
C) Lognormal
D) Normal
Q4) When considering drift and noise,how would you explain price movements over smaller and smaller time intervals?
Q5) Define the term drift.
Q6) Provide a definition of Brownian motion.
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Chapter 21: The Black-Scholes-Merton Equation
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Q1) Lapel Inc.stock price is $32.00.Joe bets Sarah that the price will be above $35.00 in 6 months (180 days).The standard deviation of the stock is 0.25 and the risk free interest rate is 5.0%.If Joe wins the bet,he wishes to be paid with one share of stock.If Sarah agrees to the bet,what is the value of her wager?
A) $3.00
B) $9.65
C) $12.44
D) $19.58
Q2) What do we call an option in which the holder has a claim that pays one share of stock if S(T)> K,and nothing otherwise?
A) Cash-or-nothing option
B) Asset-or-nothing option
C) Exotic option
D) Digital cash
Q3) Give an example of currency translation that is a change in numeraire.
Q4) How does a dividend payment impact the option price?
Q5) Briefly define a terminal boundary condition.
Q6) Explain the relationship between strike prices and implied volatilities under a price jump scenario.
Page 23
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Chapter 22: Risk-Neutral and Martingale Pricing
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Q1) The risk-neutral measure arises when we select ________ as the numeraire.
A) Asset portfolio
B) Corporate bond
C) Treasury bond
D) Money market account
Q2) It can be said that Girsanov's theorem shows the equivalence of which two items?
A) Change of drift and change of measure
B) Change of numeraire and change of measure
C) Change of drift and change of numeraire
D) Change of numeraire and change of process
Q3) When defining a change in measure,a redefining of the units in which a payoff is measured is called:
A) Brownian motion
B) Change of numeraire
C) Stochastic discount factor
D) Utility function
Q4) What aspect of risk-neutral pricing valuation links it to portfolio selection?
Q5) How do probabilities change with a change of measure?
Q6) In the first-order condition for portfolio selection,explain the meaning of equilibrium.
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Chapter 23: Exotic Options: 2
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Q1) A multivariate option that has a claim with a payoff dependent upon the price of two different assets is known as:
A) Exotics
B) Multioptions
C) Quantos
D) Supershares
Q2) In a specific wager,Pat is paid $5.00 if the price of ABC Corp.is above $85.00.Currently,ABC Corp.price is $75.00, = 0.25,r = 0.04,div = 0 and the wager lasts 6 months.If the price is below $85.00,Pat must pay $5.00.What is the net value of Pat's wager?
A) -$2.49
B) +$2.49
C) -$1.50
D) +$1.50
Q3) Donald Trump offers to give you a partnership share in his casinos if the price of his shares drops below a certain level.He charges a nominal fee for this right.What is he offering you and is he wise?
Q4) What is the risk a U.S.investor faces when investing in foreign index securities,besides index fluctuations?
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Chapter 24: Volatility
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Q1) Explain the pattern of implied volatility that is often referred to as a smirk.(Use a call as your example.)
Q2) A forward contract that pays the difference between a forward price and some measure of the realized stock variance is called a Variance:
A) Skew
B) Smile
C) Surface
D) Swap
Q3) A stock price has a historical volatility of 24%.If an anomalous event occurs to the company in the next past two days,which was not anticipated,what is the most likely implied estimate of the unconditional volatility using the GARCH model?
A) 12%
B) 20%
C) 27%
D) 45%
Q4) Why would an exponentially weighted moving average be a more accurate means of calculating volatility than a simple sampling of historical data?
Q5) What is the primary difference between ARCH models and GARCH models?
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Chapter 25: Interest Rate and Bond Derivatives
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Q1) Assume a = 0.10,b = 0.15,r = 0.04 and = 0.35.Using the CIR model,calculate the price of a zero coupon bond maturing in 6 years.
A) 0.6042
B) 0.7042
C) 0.8042
D) 0.9042
Q2) Zero-coupon bonds maturing in 1,2,and 3 years have prices of 0.9020,0.8320,and 0.7620,respectively.What is the implied forward rate from year 2 to year 3?
A) 7.94%
B) 9.19%
C) 09.68%
D) 10.21%
Q3) What is the transaction that results within an interest rate cap to make the holder's rate "capped"?
Q4) Under what conditions does delta-gamma-theta approximate the exact bond price change?
Q5) How does the node configuration in interest rates and bonds differ from stocks?
Q6) Describe the effectiveness of duration as a tool in hedging bonds.
Q7) What is calibration?
Page 27
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Chapter 26: Value at Risk
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21 Verified Questions
21 Flashcards
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Sample Questions
Q1) Why is VaR an important tool in measuring risk? What are some of its shortcomings? Ask the class to explain the rationale for a company to rely heavily on VaR in the absence of other measurement tools.
Q2) A stock has a price of $50 and pays no dividend.The historical standard deviation of the stock is 25% and the expected return on the stock is 12%.At the 95% confidence level,what is the Tail VaR over the next 6 months?
A) $2.50
B) $13.63
C) $22.36
D) $47.50
Q3) You own $4 million of Jacko Corp.The expected return is 14.0% and = 0.20.What is the value at risk over 4 weeks at a 99% confidence level?
A) $383,000
B) $413,000
C) $453,000
D) $473,000
Q4) How is VaR used in credit risk scenarios?
Q5) Why is recent data more relevant than older data when calculating volatility?
Q6) What is bootstrapping and what is its use?
Page 28
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Chapter 27: Credit Risk
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18 Verified Questions
18 Flashcards
Source URL: https://quizplus.com/quiz/32237
Sample Questions
Q1) A firm has a single issue of a zero coupon debt that promises to pay $90 in 4 years,and the A = $100,r = 5%, = 15%,and = 0.If the asset has no chance of total default,what is the value of the debt?
A) $67.10
B) $75.19
C) $85.62
D) $90.00
Q2) A bond has a current value of $950 and promises to pay $1,000 at the end of 4 years.The expected return on the asset is 12% and the risk free rate is 3%.If the actual cash payout in case of default is 0,what is the true default probability given that the asset has a standard deviation of 18%?
A) 15.2%
B) 21.5%
C) 33.2%
D) 49.6%
Q3) What are the two ways that the payoff conditional on default can be expressed?
Q4) What is the recovery rate?
Q5) What is meant by the phrase "tranche" when referring to collateralized debt obligations?
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