Risk Management
Textbook Exam Questions
Course Introduction
Risk Management is a comprehensive course that explores the principles, frameworks, and practices essential for identifying, assessing, and mitigating risks in various organizational contexts. Students will learn to analyze the multifaceted nature of risks financial, operational, strategic, and compliance-related and develop skills to create effective risk management plans. The course covers key concepts such as risk assessment techniques, risk control strategies, regulatory requirements, insurance, crisis management, and the role of risk culture in decision-making. Through practical case studies and scenario analysis, students acquire the tools necessary to anticipate potential threats and implement proactive measures to protect assets, ensure business continuity, and foster organizational resilience.
Recommended Textbook
Derivatives 2nd Edition by Rangarajan Sundaram
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791 Verified Questions
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Page 2
Chapter 1: Overview
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Q1) An embedded option is one where the security contains features that are option-like.Which of the following is not an example of a security with an embedded option?
A)Callable bond.
B)Convertible bond.
C)Mortgages in the US.
D)Preferred stock.
Answer: D
Q2) A forward contract may be used for
A)Hedging price exposure at a future date.
B)Speculating on price.
C)Locking-in a price for a future transaction.
D)All of the above.
Answer: D
Q3) A derivative security derives its value from an "underlying" security that is A)Any other security.
B)Other securities that are not derivatives.
C)Securities that are related to the "underlying" security.
D)None of the above.
Answer: A
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Chapter 2: Futures Markets
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Sample Questions
Q1) Plutonium is trading at a one-year futures price of $5,000 per gram.A futures contract comprises 100 grams.The initial margin is $100,000 and the maintenance margin is $80,000.You are short one futures contract.There is a margin call when the price per gram of plutonium changes to
A)$4,750
B)$4,900
C)$5,100
D)$5,250
Answer: D
Q2) When the futures-spot basis weakens
A)The difference between futures and spot prices drops.
B)The correlation between changes in futures and spot prices drops.
C)A hedger experiences more risk.
D)A hedger loses money on the hedge.
Answer: A
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4
Chapter 3: Pricing Forwards and Futures I
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Q1) The US dollar-euro spot exchange rate is $1.50/ .If the one-year simple interest rate on dollars is 1% and on euro is 2%,what is the one-year forward rate of dollars per euro?
A)1.4748
B)1.4853
C)1.5000
D)1.5149
Answer: B
Q2) The replication method identifies the price of a USD/GBP forward rate as a function of
A)The expected future USD/GBP exchange rate,the GBP interest rates,and the USD interest rates
B)The spot USD/GBP exchange rate and the volatility of the spot USD/GBP exchange rate
C)The spot USD/GBP exchange rate,the GBP interest rates,and the USD interest rates
D)Only the spot USD/GBP exchange rate
Answer: C
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5
Chapter 4: Pricing Forwards Futures II
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Q1) Which of the following statements about index futures is false?
A)Index futures are cash-settled.
B)Index futures track the underlying index.
C)Index futures are rarely shorted because it is very difficult to borrow all the stocks in the index in the correct proportions in order to effect the short.
D)Index futures are marked-to-market daily.
Q2) A commodity has a spot price of $25 and a one-month forward price of $25.02.The one-month risk-free rate is 2% in continuously compounded and annualized terms.Assuming no other costs or benefits of carry on the commodity,what must be the lower bound on the convenience yield that prevents arbitrage?
A)0%
B)1%
C)2%
D)3%
Q3) Backwardation becomes more likely when,ceteris paribus,
A)The dividend rate declines.
B)Storage costs increase.
C)Convenience yields decline.
D)Interest rates decline.
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Page 6
Chapter 5: Hedging With Futures Forwards
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Q1) What must be the daily interest rate (expressed in continuously-compounded and annualized terms)for the tailed hedge ratio to be 90% of the untailed one for a one-year hedge? Assume a hedging horizon of 365 days.
A)10%
B)15%
C)20%
D)25%
Q2) If changes in spot and futures prices have a correlation of \(- 1\) ,then
A)The hedge ratio is \(- 1\)
B)The variance of cash flows from a hedged position under the minimum-variance hedge ratio is zero.
C)The net cash flow at maturity of the hedge is zero.
D)The standard deviation of spot price changes must equal the negative of the standard deviation of futures price changes.
Q3) The tailed hedge ratio becomes lower in comparison to the untailed one when
A)Interest rates rise and hedge maturity increases.
B)Interest rates rise and hedge maturity decreases.
C)Interest rates fall and hedge maturity increases.
D)Interest rates fall and hedge maturity decreases.
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Page 7
Chapter 6: Interest-Rate Forwards Futures
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Q1) When you are short a position in a \(3 \times 6\) FRA,you are effectively
A)Long the three-month zero-coupon bond,and long the six-month zero-coupon bond.
B)Long the three-month zero-coupon bond,and short the six-month zero-coupon bond.
C)Short the three-month zero-coupon bond,and long the six-month zero-coupon bond.
D)Short the three-month zero-coupon bond,and short the six-month zero-coupon bond.
Q2) Bonds A and B both have a duration of exactly one year.An equally-weighted portfolio of these bonds will have a duration of
A)Greater than 1 year because duration is additive.
B)Equal to one year because the average duration is still one year.
C)Less than one year,because duration is a measure of risk,and combining two bonds into a portfolio diversifies away risk.
D)Cannot say because the outcome depends on the interaction of specific cash flows of both bonds.
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8
Chapter 7: Options Markets
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Q1) If you expect stock volatility to rise but have no particular view of direction,then you should
A)Sell stock now.
B)Sell call options.
C)Buy put options.
D)All of the above.
Q2) For a call and a put written on the same underlying but at at possibly different strike prices,
A)Both call and put options may be in-the-money at the same time.
B)If the call is in-the-money,then the put will be out-of-the-money.
C)If one of the options is out-of-the-money,then the other one is guaranteed to be in-the-money.
D)At least one option will be in-the-money.
Q3) You have a portfolio with long positions in both puts and calls.The volatility in the market rises.
A)Your portfolio gains in value.
B)Your portfolio gains on the calls and loses on the puts.
C)Your portfolio gains on the puts and loses on the calls.
D)Your portfolio is now more risky and is therefore worth less than before.
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Page 9
Chapter 8: Options: Payoffs Trading Strategies
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Q1) If you are interested in creating a retirement portfolio where the downside is protected and you retain at least some upside,the following portfolio will be consistent with your goal:
A)A long stock position plus a long collar position.
B)A short position in a protective put structure.
C)A long position in a covered call structure.
D)A short collar.
Q2) Suppose you are short a call and long a put on the S&P 500 index with the same strike and same maturity.Then,you are essentially holding
A)A long forward on the S&P 500 index
B)A long straddle on the S&P 500 index
C)A short forward on the S&P 500 index
D)A short straddle on the S&P 500 index
Q3) A long position in a strangle is:
A)A short squeeze on a straddle.
B)Worth more than a straddle whose strike lies within that of the strangle.
C)Worth less than a straddle whose strike lies within that of the strangle.
D)A choke hold on someone else's throat.
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Chapter 9: No-Arbitrage Restrictions
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Q1) There are three- and six-month American calls on \(A B C\) stock.Suppose the three-month option costs $5 and the six-month option costs $3.Which of the following statements is most accurate given this information?
A)There is an arbitrage strategy which involves buying the three-month call and selling the six-month call.
B)There is an arbitrage strategy which involves buying the six-month call and selling the three-month call.
C)There is no arbitrage available in this setting.
D)If there is a sufficiently large dividend payment between three and six months,there is no arbitrage in this situation.
Q2) A "no-arbitrage restriction" on option prices is the statement that
A)Options on possibly different stocks that trade at the same price must have the same payoffs.
B)An option written on a specific stock will be perfectly correlated with the stock.
C)The price of an option is such that no strategy can be constructed using the option and the underlying that generates arbitrage profits.
D)Arbitrage trading in options is prohibited by the SEC.
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Page 11
Chapter 10: Early-Exercise/Put-Call Parity
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Q1) If the interest rate is positive,then which of the following statements is valid for at-the-money call and put options written on the same underlying stock for the same strike and maturity?
A)The call is worth more than the put.
B)The call price is equal to the put price.
C)The call price is less than the put price.
D)More information is needed to determine the relative values of the call and put.
Q2) Consider a portfolio comprised of a short call and a short put,both options written on the same stock,same strike,and for the same maturity.Which of the following is valid?
A)The intrinsic value of the portfolio is zero.
B)The time value of the portfolio is zero.
C)The insurance value of the portfolio is negative.
D)All of the above.
Q3) Given that call prices are convex in strike prices,the implication is that
A)Put prices are concave in strike prices.
B)Put prices are linear in strike prices.
C)Put prices are convex in strike prices.
D)Put prices may be convex or concave in strike prices.
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Chapter 11: Option Pricing: An Introduction
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Q1) In a one-period binomial model,assume that the current stock price is $100,and that it will rise to $110 or fall to $90 after one month.What is the delta of a 99-strike one-month put option?
A) \(- 0.50\)
B) \(- 0.45\)
C) \(+ 0.45\)
D) \(+ 0.50\)
Q2) In a one-period binomial model,assume that the current stock price is $100,and that it will rise to $110 or fall to $90 after one month.If the risk-neutral probability of the stock going up or down is equal,what is the one-month risk-free interest rate in continuously-compounded and annualized terms?
A)0%
B)1%
C)2%
D)3%
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13
Chapter 12: Binomial Option Pricing
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Q1) A stock is currently trading at $100.In each month,the stock will either increase in price by a factor of \(u = 1.10\) or fall by a factor of \(d = 0.90\) .The risk-free rate of interest per month is 0.1668% in simple terms,i.e. ,an investment of $1 at the risk-free rate returns $1.001668 after one month.What is(a)the price of a 100-strike,three-month European put option,and(b)the price of a 100-strike,two-month European put option?
A)$7.20 and $5.41,respectively.
B)$7.20 and $5.08,respectively.
C)$5.08 and $7.70,respectively.
Q2) A stock is currently trading at $100.In each month,the stock will either increase in price by a factor of \(u = 1.10\) or fall by a factor of \(d = 0.90\) .The risk-free rate of interest per month is 0.1668% in simple terms,i.e. ,an investment of $1 at the risk-free rate returns $1.001668 after one month.What is the price of a 100-strike,six-month European call option when a dividend of $1 is paid at the end of each month? (Assume that if the option is exercised,it is done just before a dividend payment. )
A)$7.20
B)$7.50
C)$7.70
D)$8.20
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Page 14
Chapter 13: Implementing the Binomial Model
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Q1) As the number of steps in the CRR binomial tree increases (keeping maturity fixed),the solution "converges" to a limit result.Which of the following statements characterizes this convergence best?
A)The solution results in the Black-Scholes formula.
B)The convergence may be oscillatory for even and odd number of steps in the tree.
C)The convergence may be monotonic for even and odd number of steps in the tree.
D)All of the above.
Q2) In the Cox-Ross-Rubinstein (CRR)binomial model,the volatility is given as \(\sigma = 0.2\) .The risk-free rate of interest is 2%.What is the risk-neutral probability of an up move on a binomial tree with a time step of one month?
A)0.45
B)0.50
C)0.55
D)0.60
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15
Chapter 14: The Black-Scholes Model
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Q1) Consider a call option on a stock that pays dividends at the rate \(q > 0\) .Which of the following statements is most valid for the Black-Scholes model?
A)The call is worth more than a call on an equivalent stock that pays no dividends.
B)The probably of the option finishing up in the money is greater than that of a call on an equivalent stock that pays no dividends.
C)The time value of the call is greater than that of a call on an equivalent stock that pays no dividends.
D)None of the above.
Q2) The current price of a stock is $100.Consider the Black-Scholes model price of a six-month call option at strike $101,given an interest rate of 2% and a dividend rate of 1%? The volatility is 25%.What is the risk-neutral probability of the option ending up in the money?
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Chapter 15: Mathematics of Black-Scholes
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Q1) Which of the following properties of a put option's beta is most valid?
A)The beta of a put increases as the stock price increases.
B)The beta of a put decreases if the beta of the stock increases.
C)The beta of a put is bounded between \(( - 1 , + 1 )\) )
D)The beta is always positive.
Q2) Consider a stock that is trading at $50.A six-month at-the-money put option on the stock has a price of 2.21 and a delta of \(- 0.40\) .The stock volatility is 20%,the risk-free rate is 4%,and the beta of the stock is 1.1.What is the beta of the put?
A) \(- 0.44\)
B) \(- 1.1\)
C) \(+ 1.1\)
D) \(- 9.95\)
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Chapter 16: Beyond Black-Scholes
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Q1) Stochastic volatility models commonly assume
A)There are jumps in the evolution of the volatility process.
B)Volatility follows a geometric Brownian motion process.
C)Volatility is normally distributed.
D)Volatility follows a mean-reverting process.
Q2) In the preceding question,the state price in the lower node after one month is equal to
A)0.4996
B)0.5000
C)0.5368
D)0.5372
Q3) GARCH models
A)Are discrete-time expressions of stochastic volatility models.
B)Are designed to capture the empirically-observed leverage effect in equity returns.
C)Are models in which volatility is not separately stochastic but evolves in a manner dependent on the stock return process.
D)Are useful for describing stock returns empirically but not for pricing options on equity.
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18
Chapter 17: The Option Greeks
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Q1) You hold a straddle on a stock that you bought a month ago and that still has two months to expiry.Assume the options are European.An unexpected increase of $1 in the price of the stock
A)Will increase the value of your straddle.
B)Will decrease the value of your straddle.
C)Will have no effect on the value of your straddle.
D)Can increase,decrease,or leave unchanged the value of the straddle.
Q2) Which of the following is NOT valid about the time decay of European put and call options with the same strike and maturity?
A)The time decay is measured in dollars per unit time.
B)The call decays at the same rate as the put.
C)The call decays faster than the put.
D)The difference between the time decay of decay of the call and put depends on the moneyness of the options.
Q3) The gamma of a put is typically highest when
A)The stock price is much lower than the strike price.
B)The stock price is in the region of the strike price.
C)The stock price is much higher than the strike price.
D)The information is insufficient to answer this question.
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Page 19
Chapter 18: Path-Independent Exotic Options
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Q1) Consider an at-the-money call option on the maximum of two assets.As the correlation between the two assets increases,what happens to the value of this option?
A)It decreases.
B)It stays the same.
C)It increases.
D)There is not enough information to answer this question.
Q2) You are long a portfolio of vanilla call options.Which of the following will help you hedge away your vega risk?
A)Buying a portfolio of in-the-money vanilla put options.
B)Buying a portfolio of out-of-the money vanilla put options.
C)Buying a portfolio of in-the-money cash-or-nothing put options.
D)Buying a portfolio of out-of-the money cash-or-nothing put options.
Q3) Consider digital (cash-or-nothing)call options.When volatility increases,the holders of out-of-the-money options generally ,and the holders of in-the-money options generally
A)benefit;benefit.
B)benefit;lose.
C)lose;benefit.
D)lose;lose.
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Page 20
Chapter 19: Exotic Options II: Path-Dependent Options
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Q1) Which of the following statements is FALSE?
A)Asian calls are always worth less than the corresponding vanilla calls.
B)Asian puts are always worth less than the corresponding vanilla puts.
C)Arithmetic-average Asian calls are always worth less than the corresponding vanilla calls but geometric-average Asian calls may be worth more.
D)At low volatilities,all Asian options are worth less than the corresponding vanilla options,but at high volatilities they may be worth more.
Q2) Which of the following statements is most valid?
A)Asian options are useful for hedging risk to markets in Asia.
B)Asian options are usually more expensive than vanilla options because they are exotic.
C)Asian options are useful for hedging exposure to the average price of a security or commodity.
D)Asian options are more sensitive to volatility than vanilla options.
Q3) An Asian option is an option where
A)The underlying is the average of the stock price for a specified period.
B)The strike price is the average of the stock price over a specified period.
C)The average can be an arithmetic or geometric average.
D)All of the above are possible in an Asian option.
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21
Chapter 20: Value at Risk
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Q1) If every position in a portfolio is doubled in size,the risk contribution of the original portion of the portfolio,as measured by VaR,will
A)Remain the same as before.
B)Double.
C)Halve.
D)More than double.
Q2) Historical simulation as a method of computing VaR has the following major benefit in comparison to the delta-normal method:
A)It is a faster approach.
B)It uses past returns to forecast future returns.
C)It requires the same number of parameters as the delta-normal method.
D)It does not assume normality of the P&L return distribution.
Q3) Monte Carlo is widely-used approach for computing VaR.Relative to other methods which of the following is a benefit of using this approach?
A)It is fully flexible in parameterizing the forward-looking distribution.
B)It always requires very few parameters.
C)It always uses normality.
D)It is the fastest approach to computing VaR.
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Chapter 21: Swaps and Floating Rate Products
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Q1) Which of the following is not an interest-rate swap?
A)A fixed-for-floating swap involving exchange of fixed interest rate payments in one currency for floating payments in the same currency but in which the swap NPV at inception is non-zero.
B)A floating-for-floating swap in which one floating rate in a currency is exchanged for another floating rate in the same currency.
C)A fixed-for-floating swap in which a fixed interest rate payment in one currency is exchanged for floating interest-rate payments in another currency.
D)A fixed-for-floating swap involving exchange of fixed interest rate payments in one currency for floating payments in the same currency but in which the payments are computed on principal that is reduced in a pre-specified manner during the life of the swap.
Q2) The UK money-market day-count convention is
A)Actual/365.
B)Actual/360.
C)Actual/Actual.
D)30/360.
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Page 23
Chapter 22: Equity Swaps
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Q1) An equity swap favors the party that receives the equity return and pays Libor because
A)Equity returns are on average higher than Libor returns.
B)The probability that equity markets beat the bond markets is greater than 50%.
C)Equities are less risky in the long run.
D)None of the above.
Q2) Consider a five-year equity swap that pays the equity return in return for six-month Libor.Which of the following statements is most valid? Assume you are at the inception of the swap.
A)The interest-rate duration of the swap is five years.
B)The interest-rate duration of the swap is six months irrespective of the correlation between interest rates and equity returns.
C)The interest-rate duration of the swap is greater than six months if the equity return is positively correlated with interest rates.
D)The interest-rate duration of the swap is greater than five years if the equity return is negatively correlated with interest rates.
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Chapter 23: Currency and Commodity Swaps
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Q1) ABC,a US-based corporation enters into a currency basis swap with XYZ,a British company,in which the initial principal amounts are $200 million and \(£\) 100 million.That is: -At inception,there is an initial principal exchange in which ABC pays XYZ $200 million and receives -- \(£\) --100 million.
-Subsequently,at each interest payment date ABC pays XYZ the GBP-Libor rate on -- \(£\) --100 million,and receives the USD-Libor rate on $200 million.
-Fnally,at maturity,a re-exchange of principals occurs in which ABC pays XYZ -- \(£\) -- 100 million in exchange for $200 million. Suppose the spot exchange rate is $1.55 = \(£\) 1 at the time of entering into the swap.Assume that ABC and XYZ both have AA credit ratings at this time and can access funds at Libor flat.Then,from a credit perspective,
A)ABC is carrying more counterparty risk than XYZ.
B)ABC is carrying less counterparty risk than XYZ.
C)Both sides are carrying the same credit risk.
D)Neither side is carrying any credit risk.
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Chapter 24: Term Structure of Interest Rates: Concepts
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Q1) The zero-coupon rate (zcr)is
A)The rate of return each period on a bond that pays no coupons.
B)The yield-to-maturity of a zero-coupon bond.
C)The return on the bond's appreciation excluding coupon payments.
D)Zero.
Q2) The 6-months risk-free zero rate is 2.84%,and the one-year zero rate is 3.17%.Assuming no-arbitrage,the yield-to-maturity on a $1,000 par of a one-year,12% Treasury bond,that pays $60 after 6 months and $1060 after one-year,must be
A)Greater than 0% and less than 2.84%
B)Greater than 2.84% and less than 3.17%
C)Greater than 3.17% and less than 6.01%
D)6.01%
Q3) If zero rates (i.e. ,discount rates)are the same for all maturities and remain the same over the next year,the price of a zero-coupon bond that matures ten years from today will:
A)Decrease over the next year
B)Remain the same over the next year
C)Increase over the next year
D)Cannot tell with the given information
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Page 26
Chapter 25: Estimating the Yield Curve
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Q1) The Nelson-Siegel algorithm is primarily used for fitting a smooth curve to the following:
A)Yields.
B)Zero-coupon rates.
C)Forward rates.
D)Discount functions.
Q2) In the cubic splines technique,which of the following is a benefit of adding more knot points to the algorithm?
A)It enhances the smoothness of the forward curve obtained from the fitted function.
B)It makes implementation easier as the number of parameters increases.
C)It increases flexibility in being able to fit a greater variety of shapes for the discount function.
D)It enables fitting the curve to more bonds and allows incorporating illiquid bonds as well.
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27
Chapter 26: Modeling Term Structure Movements
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Q1) The term "no-arbitrage" class of term-structure models refers to
A)Models which focus on bond prices directly rather than interest rates.
B)Models which work under the martingale measure directly rather than under the actual or "statistical" measure.
C)Models whose parameters never have to be re-estimated since no-arbitrage ensures that they cannot change from day to day.
D)Models which are capable of matching the observed term-structure perfectly.
Q2) "No-arbitrage" models of the interest rate differ from "equilibrium" models of the interest rate in that
A)They have a larger number of free parameters enabling them to fit the yield curve exactly.
B)They do not admit arbitrage whereas an equilibrium model may admit arbitrage under some conditions.
C)Equilibrium models were derived in the academic literature whereas whereas no-arbitrage models were developed mainly by practitioners.
D)They allow for the possibility that the market is in disequilibrium
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Chapter 27: Factor Models of the Term Structure
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Q1) Assume annual compounding.The one-year and two-year zero-coupon rates in the BDT model are 6% and 7%.The volatility is given to be \(\sigma = 0.30\) .What is the price of a one-year maturity call option on a 7.5% coupon (annual pay)bond at a strike of $100 (ex-coupon)?
A)0.80
B)0.90
C)1.00
D)1.10
Q2) A one-factor bond pricing model implies that interest-rates of all maturities are driven by a single source of stochastic randomness.For example the system of interest rates may be described by the following equation: \(d r ( T ) = \alpha ( r ( T ) , T ) d t + \sigma ( r ( T ) , T ) d W , \quad \forall T\) where \(T\) denotes the maturity of different rates.A single-factor model implies that
A)All rates either move up together or all move down together.
B)The yield curve experience parallel shifts.
C)Instantaneous changes in rates of all maturities are perfectly positively or negatively correlated with each other.
D)Twists in shape of the yield curve are not possible.
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Chapter 28: The Heath-Jarrow-Morton Hjmand Libor
Market Model LMM
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Q1) Consider a one-factor HJM model where the initial forward curve is given as 6% for one year and 7% between one and two years.The evolution of continuously-compounded one-year forward rates beginning at time \(T\) ,is given by the following binomial process: \(f ( t + 1 , T ) = f ( t , T ) + \alpha \pm 0.02\) ,where the up and down movements are equiprobable.Consider the price of one-year call and put options on a two-year 6.5% coupon bond,with a strike price of $100 ex-coupon.The difference between the call and put prices will be A) \(6.5
C) \(106.5 e ^ { - 0.06 - 0.07 } - 100 e ^ { - 0.06 } - 6.5 e ^ { - 0.06 }\) D) \(106.5 e ^ { - 0.06 - 0.07 } - 100 e ^ { - 0.06 }\)
Q2) Which of the following is not a valid property of the Heath-Jarrow-Morton (HJM)interest-rate framework?
A)The model may be calibrated to be consistent with any initial yield curve.
B)The tree version of the model has rates of all remaining maturities at each node of the tree.
C)The model fits volatilities of rates of all maturities.
D)The model is a one-factor model.
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Chapter 29: Credit Derivative Products
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Q1) Bank A holds a credit risky asset on its balance sheet.It enters into a total return swap (TRS)referenced to this asset with hedge fund B to pay the total return to B and receive Libor in return.Under what scenario does bank A bear credit risk on the reference asset this contract?
A)When the issuer of the reference asset defaults.
B)When hedge fund B defaults.
C)Only when the issuer of the reference asset and hedge fund B default.
D)All of the above.
Q2) Which of the following factors contributed to the the substantial growth in the market for credit derivatives in the 2000s?
A)Extensive growth in debt markets.
B)Disintermediation of banks.
C)Increases in regulation of securities markets,investors,and issuers.
D)All of the above.
Q3) What action is involved in constructing a synthetic CDO?
A)Selling protection via CDS contracts.
B)Buying protection via CDS conracts.
C)Selling tranches of other CDOs.
D)Buying a diversified equity portfolio.
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Page 31
Chapter 30: Structural Models of Default Risk
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Q1) Suppose the current value of a firm's assets is $100 million,and the value of equity in the firm is $40 million.Suppose too that the firm has only one issue of debt outstanding: zero-coupon debt with a maturity of three years,and a face value of $70 million.Finally,suppose that the risk-free rate of interest is 4% (continuously-compounded terms)for all maturities.Assuming that firm value evolves according to a lognormal diffusion (as in Merton,1974),what is the volatility of the firm's assets?
A)10.0%
B)19.2%
C)24.2%
D)35.4%
Q2) A firm has one-year zero-coupon debt with face value $7 billion.Assuming the firm value at the end of the year is normally distributed with a mean of 10 billion and a standard deviation of 2 billion,,what is the probability that the firm's assets will not be sufficient to repay the debt at the end of the year?
A)0.14%
B)4.44%
C)5.39%
D)6.68%
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Chapter 31: Reduced-Form Models of Default Risk
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Q1) Consider a one-year zero-coupon defaultable bond.Let \[r\] and \[S\] denote,respectively,the risk-free interest rate and the spread on the bond,where both are expressed in simple terms with annual compounding.Suppose the risk-neutral probability of default \[\lambda\] and the recovery rate of the bond in default \[\phi\] remain fixed.Then,an increase in the risk-free rate must be accompanied by
A)An increase in the spread.
B)A decrease in the spread.
C)No change in the spread.
D)A change in the spread that can be positive,negative,or zero.
Q2) Suppose we have a zero-coupon bond that pays $1 after one year if the issuing firm is not in default.If the firm is in default the recovery rate is 40%.The one-year risk free interest rate in simple terms is 5% and the risk-neutral probability that the firm defaults is 10%.What is today's fair price for this bond?
A)$0.875
B)$0.895
C)$0.915
D)$0.935
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Chapter 32: Modeling Correlated Default
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Q1) The difference between implied correlation and base correlation in CDOs is that
A)Base correlation is the smallest correlation implied across all tranches of a CDO.
B)Base correlation is the correlation of cumulative sets of tranches starting with the equity tranche,whereas implied correlation is for single tranches only.
C)All base correlations are implied,but not all implied correlations are base correlations.
D)Base correlation is historical and implied correlation is computed using tranche prices at a point in time.
Q2) Consider two firms with one-year probabilities of default of \[p _ { 1 } = 0.10\] and \[p _ { 2 } = 0.05\] ,respectively.The conditional probability of default in one year is \[\operatorname { Pr } \left[ D _ { 1 } \mid D _ { 2 } \right] = 0.7\] .What is the probability of a first-to-default basket option that pays $100 if any one firm defaults within a year? (Assume zero discount rates. )
A)$10.00
B)$11.50
C)$14.25
D)$17.35
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