Asset Pricing Study Guide
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Course Introduction
Asset Pricing explores the fundamental principles and models used to determine the value of financial assets in competitive markets. The course covers both theoretical and empirical approaches to asset valuation, including the time value of money, risk and return, portfolio theory, capital asset pricing models (CAPM), arbitrage pricing theory (APT), and market efficiency. Students will analyze how information, expectations, and market structures impact asset prices, and assess the implications for investment and risk management decisions. The curriculum is designed to provide a rigorous framework for understanding how securities are priced and how these prices reflect the underlying economic fundamentals.
Recommended Textbook Derivatives 2nd Edition by Rangarajan Sundaram
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Chapter 1: Overview
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Q1) Which of the following statements is true of the value of European (E)options,American (A)options,and Bermudan (B)options?
A) \(A > B > E\)
B) \(A > E > B\)
C) \(E > A > B\)
D) \(B > A > E\)
Answer: A
Q2) State which of these statements is false.
A)A futures contract is traded on an exchange.
B)A futures contract involves counterparty credit risk.
C)A futures contract is fully customizable.
D)A futures contract may be reversed unilaterally.
Answer: C
Q3) Which of the following securities is not a derivative?
A)Call option on a stock.
B)A bond issued by a BBB-rated corporate firm.
C)Put option on a currency.
D)A futures contract on oil.
Answer: B
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Chapter 2: Futures Markets
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Q1) A price tick is
A)The maximum amount by which the price can move in a day.
B)The minimum amount by which the price can move.
C)The bid-ask spread on the price.
D)The minimum amount of trading required on the exchange per trade.
Answer: B
Q2) The most widely traded futures are of the following type:
A)Equity.
B)Interest rate.
C)Agricultural.
D)Commodity.
Answer: B
Q3) March what futures are trading at $4.20 a bushel and May wheat futures are trading at $4.35 a bushel.You expect the spread between May and March futures prices to widen.To speculate on this view,you would
A)Go long March futures and short May futures.
B)Go long May futures and short March futures.
C)Go long May futures.
D)Go long March futures.
Answer: B
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Chapter 3: Pricing Forwards and Futures I
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Q1) Two assets \(A\) and \(B\) have the same spot price today.The price of asset \(A\) is expected to grow at 10% over the next year and that of asset \(B\) is expected to grow at 10% also.Asset \(A\) has a standard deviation of returns of 10% over the year and asset \(B\) has standard deviation of 15%.Which of the following is true if there are no holding costs or benefits?
A)Asset \(A\)
's one-year forward price will be less than that of asset \(B\)
B)Asset \(A\)
's one-year forward price will be greater than that of asset \(A\)
C)Asset \(A\)
's one-year forward price will be equal to that of asset \(B\)
D)Any of the above may be true.
Answer: C
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5
Chapter 4: Pricing Forwards Futures II
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Q1) If there is a convenience yield,then the following is true of the forward price:
A)The forward price is higher than it would be if there were no convenience yield.
B)The bid price may be higher than the ask price on the forward.
C)The forward price does not depend on the convenience yield.
D)The forward price is lower than it would be with no convenience yield.
Q2) For commodity forwards and futures,which of the following statements is valid?
A)The presence of a convenience yield means that the market will be in contango.
B)Convenience yields may lead to the market being in backwardation.
C)If there are storage costs,the convenience yield is zero-it is no longer convenient to hold the commodity.
D)As supply becomes plentiful,convenience yields will rise.
Q3) Two stocks,A and B,have expected returns for one year of \(- 10 \%\) and \(+ 10 \%\) respectively.The stocks have identical prices of $100 each,do not pay dividends,and the one-year risk-free rate of return is 2% in simple terms.The one-year forward prices of the two stocks are:
A)A: 90;B: 110
B)A: 92;B: 112
C)A;102;B: 102
D)A: 112;B: 112
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Page 6
Chapter 5: Hedging With Futures Forwards
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Q1) 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.
Q2) If the minimum-variance hedge ratio is \(- 1\) ,then which of the following statements is true?
A)Changes in spot and futures prices are perfectly negatively correlated.
B)The standard deviations of spot and futures price changes are the same.
C)The minimum-variance hedge for a long spot exposure is a short futures exposure of the same size.
D)All of the above.
Q3) 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.
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Page 7
Chapter 6: Interest-Rate Forwards Futures
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Q1) You are given the following data concerning a 6×12 FRA.The first six-month period is 182 days and the second is 183 days.The Libor rate for six months is 5% and for one year is 6%.The arbitrage-free price of the 6×12 FRA,assuming the Actual/360 day-count convention,is
A)5.50%
B)6.22%
C)6.55%
D)6.82%
Q2) Consider a 6×12 FRA where the underlying six-month period is 183 days and the notional is $100.The FRA fixed rate is 5%.At maturity of the contract the underlying Libor for six months is 7%.What is the settlement amount on the FRA? Assume the Actual/360 convention.
A)0.9683
B)0.9687
C)0.9817
D)1.0167
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Chapter 7: Options Markets
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Q1) If your directional view is that stock prices are going to fall,you should
A)Sell stock now.
B)Sell call options.
C)Buy put options.
D)All of the above are profitable strategies.
Q2) You have $100 to invest in a stock (or options on the stock).The stock is trading for $100.The three-month 100-strike calls on the stock are trading at $4 each.The minimum stock price you expect to see after three months is $60.What is the worst case return on investment you can possibly end up with using stock and/or options?
A)-100%
B)-40%
C)0%
D)+6%
Q3) 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.
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Page 9
Chapter 8: Options: Payoffs Trading Strategies
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Q1) Consider a ratio spread comprising a call at strike \(K _ { 1 }\) and short two calls at strike \(K _ { 2 } > K _ { 1 }\) .The current stock price is at \(K _ { 1 }\) .The market view for this trade is most likely to be:
A)That the stock is more likely to fall in price than rise in price.
B)That volatility of the stock is likely to rise.
C)That the stock is likely to experience high levels of positive skewness in returns.
D)That the stock will rise but not by an indefinite amount.
Q2) You are long an at-the-money straddle on a stock index.Which of the following statements is valid?
A)Your position increases in value if,ceteris paribus,the index rises.
B)Your position increases in value if,ceteris paribus,the index falls.
C)Your position increases in value if,ceteris paribus,the volatility of the index rises.
D)All of the above.
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Chapter 9: No-Arbitrage Restrictions
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Q1) The current price of a non-dividend paying stock is $40.A European call option with three months maturity and strike $39 is priced at $2.The risk free rate of interest for three months is 2%.Which of the following statements is correct?
A)The price of the call obeys no-arbitrage restrictions.
B)It is possible to construct a risk-less arbitrage strategy to yield a gain of at least $0.81.
C)It is possible to onstruct a risk-less arbitrage strategy to yield a gain of at least $1.00.
D)It is possible to construct a risk-less arbitrage strategy to yield a gain of at least $1.19.
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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Chapter 10: Early-Exercise/Put-Call Parity
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Q1) The stock price is $30.The strike price of a three-month European put option is $32.If the put option is priced at $5,and the risk-free rate of interest is 2%,and the stock pays no dividends,then the insurance value of the option is
A)1.84
B)2.00
C)3.16
D)4.96
Q2) An American call option on a stock that pays no dividends:
A)May be exercised early if the stock rises sharply just before maturity.
B)Is always exercised early when the the call is deep in-the-money,and the volatility of the stock drops from its initial level.
C)Is not exercised early unless the growth in the stock exceeds the rate of interest.
D)Is never exercised early.
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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Page 12
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.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%
Q2) You hold a portfolio consisting of 300 calls (short)and 200 puts (long)on a given stock.The delta of the calls is \(+ 0.62\) and the delta of the puts is \(- 0.57\) .To delta hedge this portfolio,you should
A)Short 74 shares of the stock.
B)Buy 300 shares of the stock.
C)Buy 500 shares of the stock.
D)Buy 74 shares of the stock.
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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 \(u = 1.05\) 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,two-month European put option?
A)$2.36
B)$3.36
C)$4.36
D)$5.36
Q2) Schroder's (1988)approach to binomial option pricing offers a way of
A)Obtaining recombining trees by restating cash dividends as dividend yields.
B)Obtaining recombining binomial trees even when there are cash dividends.
C)Obtaining recombining trees when dividends are stated as yields but not when they are stated as cash amounts.
D)Pricing options efficiently using non-recombining binomial trees.
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Page 14
Chapter 13: Implementing the Binomial Model
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Q1) Which of the following statements is most valid for the recursive programming of a binomial tree for pricing options?
A)The recursive program requires more lines of code than a non-recursive loop-driven program.
B)The recursive program requires less computer memory than a non-recursive loop-driven program.
C)The recursive program runs slower than a non-recursive loop-driven program.
D)The recursive program runs in polynomial time whereas a non-recursive loop-driven program runs in exponential time.
Q2) Suppose returns on a stock are lognormally distributed with expected (annualized)mean of of 0.10 and standard deviation of 0.20.What is the standard deviation of the continuously compounded return on the stock for one month?
A)1.77%
B)3.33%
C)5.77%
D)7.33%
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Chapter 14: The Black-Scholes Model
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Q1) The three-month S&P 500 futures contract is trading at a level of 1250.The rate of interest is 2%.The average rate of dividends for stocks in the index is 3%.Index volatility is 20%.What is the Black-Scholes price of a one-year at-the-money put option on the futures?
A)$97.34
B)$97.60
C)$98.33
D)$99.12
Q2) The current price of a stock is $100.What is 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%.
A)$6.30
B)$6.52
C)$6.56
D)$6.78
Q3) Which of the following is not an assumption underlying the Black-Scholes model?
A)The rate of interest is constant.
B)The dividend rate must be less than the interest rate.
C)Stock volatility is constant.
D)There are no taxes and transactions costs.
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Chapter 15: Mathematics of Black-Scholes
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Q1) Consider a stock that is trading at $50.A six-month at-the-money call option on the stock has a price of 3.45 and a delta of 0.60.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 call?
A)0.66
B)1.1
C)9.56
D)15.94
Q2) 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.
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Chapter 16: Beyond Black-Scholes
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Q1) A stock has a current price of $100.Assume a CRR-style jump-to-default model in which the volatility is 30%.Let the risk-neutral probability of default in three months be 10%.The 3-month risk-free rate is 2% in continuously-componded and annualized terms.What is the price of a three-month at-the-money put option on this stock in a one-period jump-to-default tree model?
A)$7.22
B)7.72
C)$11.82
D)$13.42
Q2) Which of the following assumptions made in deriving the Black-Scholes formula are commonly violated in the real world?
A)Log-returns are normally distributed.
B)The volatility of the stock is constant.
C)Prices evolve continuously,i.e. ,there are no market "gaps."
D)All of the above.
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18
Chapter 17: The Option Greeks
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Q1) You hold a portfolio of a long position in a call and a short position in a put,both for the same strike and maturity,both written on a non-dividend paying stock.Which of the following statements is most correct?
A)The delta of the portfolio increases when the stock price increases.
B)The delta of the portfolio stays the same when the stock price increases.
C)The delta of the portfolio decreases when the stock price increases.
D)The delta of the portfolio may increase or decrease when the stock price increases.
Q2) The vega of a ________ is highest when it is_________.
A)call;deep in-the-money.
B)put;deep out-of-the-money.
C)call or put;far away-from-the-money.
D)None of the above.
Q3) For options that are at-the-money,which of the following statements is typically valid as maturity nears?
A)Gamma increases as does theta.
B)Gamma increases and theta decreases.
C)Gamma decreases and theta increases.
D)Gamma and theta both decrease.
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Chapter 18: Path-Independent Exotic Options
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Q1) You have written a put on a put,where the underlying put is written on a stock index.To delta hedge yourself you can either go the underlying put or the underlying index.
A)short;short.
B)short;long.
C)long;short.
D)long;long.
Q2) 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.
Q3) Consider the following compound options written on an underlying stock.Which one decreases in value when the stock falls in price?
A)A put on a call.
B)A call on a put.
C)A put on a put.
D)None of the above.
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Chapter 19: Exotic Options II: Path-Dependent Options
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Q1) Consider the following at-the-money options,all of the same maturity: a vanilla European call ( \(C _ { E }\) ),an American vanilla call ( \(C _ { A }\) ),a fixed-strike lookback call ( \(C _ { L }\) ).Which of the following is correct?
A) \(C _ { L } \leq C _ {E } \leq C _ { A }\).
B) \(C _ { L } \leq C _ {E } \leq C _ { A }\)
C) \(C _ {E } \leq C _ { A } \leq C _ { L }\)
D) \(C _ { A } \leq C _ { E } \leq C _ { L }\).
Q2) In a barrier option,
A)Price paths are bounced off the barrier.
B)Option payoffs are conditional on whether the underlying breached the barrier during the option's life.
C)Option payoffs are conditional on when the underlying breached the barrier during the option's life.
D)Conditional on the barrier being breached during the option's life,option payoffs differ based on how many times the barrier was breached.
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21
Chapter 20: Value at Risk
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Q1) 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.
Q2) "Monotonicity" is the requirement of a risk-measure that if Portfolio A dominates Portfolio B (in the sense of always doing at least as well as B in every state of the world and strictly better in some states),then the risk of Portfolio A should be less than the risk of Portfolio B.Which of the following statements is correct?
A)Standard deviation (SD)fails to satisfy monotonicity.
B)Value-at-Risk (VaR)fails to satisfy monotonicity.
C)Expected shortfall (ES)fails to satisfy monotonicity.
D)All three of these portfolio risk-measures (SD,VaR,and ES)fail monotonicity.
Q3) The value-at-risk of a portfolio is
A)Always positive.
B)Always negative.
C)May be positive or negative.
D)Always non-negative.
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Page 22
Chapter 21: Swaps and Floating Rate Products
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Q1) Consider a one-year caplet on underlying six-month Libor at a strike rate of 6%.If the corresponding floorlet is equal to the caplet in price,what is the current forward rate for the period (1,1.5)years?
A) \(< 6 \%\)
B) \(= 6 \%\)
C) \(> 6 \%\)
D)Cannot be determined from the given information.
Q2) The US Treasury market day-count convention is
A)Actual/365.
B)Actual/360.
C)Actual/Actual.
D)30/360.
Q3) Choose the most appropriate of the following alternatives: an off-market swap is one where the fixed rate in the swap is
A)Higher than the prevailing swap rate.
B)Lower than the prevailing swap rate.
C)Equal to the prevailing swap rate.
D)Different from the prevailing swap rate.
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Chapter 22: Equity Swaps
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Q1) An equity swap may be used to time the markets.Given a current position in a $1,000 portfolio of 80:20 (equity:bonds),suppose you expect that bonds will perform relatively better than stocks and want to change the portfolio composition to 20:80,what swap would you enter into?
A)An equity swap to receive the equity return and pay the bond return for a notional of $1,000.
B)An equity swap to pay the equity return and receive the bond return for a notional of $1,000
C)An equity swap to receive the equity return and pay the bond return for a notional of $600.
D)An equity swap to pay the equity return and receive the bond return for a notional of $600
Q2) Which of the following factors does not affect the valuation of a variable notional equity swap that pays the equity return in exchange for Libor?
A)Expected equity price growth.
B)Equity volatility.
C)Interest-rate term structure.
D)All of the above.
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Page 24
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) If the forward rate curve is downward sloping,then
A)The zero-coupon curve will lie above the yield curve.
B)The zero-coupon curve will lie below the yield curve.
C)The zero-coupon curve will lie above the yield curve in the near maturities and then lie below the yield curve for later maturities.
D)Not enough information to be able to answer the question.
Q2) 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.
Q3) The "rule of 72" states that invested money doubles in value if the product of the interest rate (in percentage form)and time invested (in years)equals 72.Assuming continuous compounding,what exactly must the product be for money to double?
A)69
B)71
C)73
D)75
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Chapter 25: Estimating the Yield Curve
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Q1) Which of the following is NOT a property of a cubic spline?
A)It is flexible concerning the number of knot points to be used.
B)It uses third-order polynomials in time \(t\)
C)There are three parameters in each function between pairs of knot points.
D)It is capable of accommodating a wide variety of shapes for the yield curve.
Q2) Under logarithmic interpolation,if he \(t _ { i }\) -tear yield is \(y \left( t _ { i } \right)\) , \(i = 1,2\) ,then the interpolated yield for \(\pm\) lying between \(t _ { 1 }\) and \(t _ { 2 }\) is given by \(y ( t ) = y \left( t _ { 1 } \right) \left[ 1 + \ln \left( 1 + x \cdot \left( t - t _ { 1 } \right) \right) \right],\) where \(x\) is a parameter.Suppose the yield at one year is 4% and the yield at two years is 5%.Then,the closest yield at one and a half years,using logarithmic interpolation in time \(t\) ,is
A)4.47%
B)4.50%
C)4.53%
D)4.55%
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Chapter 26: Modeling Term Structure Movements
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Q1) Which of the following is not sufficient for a pricing tree for risky bonds to be free of arbitrage?
A)The existence of a risk-neutral pricing probability measure.
B)The existence of a general equilibrium in the asset markets.
C)All normalized (discounted)assets are martingales.
D)On the tree,the gross risk-free one-period return is straddled by the return when rates move up and when rates move down.
Q2) "Equilibrium" models of the term-structure
A)Are general equilibrium models of all securities in the economy.
B)Are models which match observed term structure curves perfectly.
C)Include such models as Vasicek (1977)and Cox,Ingersoll,and Ross (185).
D)Are models which ensure that "disequilibrium" phenomena,such as negative interest rates,cannot occur.
Q3) In the Black-Scholes formula,interest rates are assumed to be constant.This is not appropriate for pricing options on bonds primarily because
A)The value of a bond is constant if interest rates are constant.
B)Constant rates would mean no volatility in bond prices and no option value.
C)Payoffs would be discounted at a constant rate.
D)None of the above.
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Page 28
Chapter 27: Factor Models of the Term Structure
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Q1) In the Vasieck (1977)model,you are given that \(d r _ { t } = k \left( \theta - r _ { t } \right) d t + \sigma d W _ { t }\) where \(x = 0.5\) , \(\theta = 0.06\) , \(\sigma = 0.10\) ,and the current short rate of interest is \(r _ { 0 } = 0.08\) .What is the expected standard deviation of the short rate of interest one year hence?
A)0.08
B)0.09
C)0.10
D)0.11
Q2) 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
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29
Chapter 28: The Heath-Jarrow-Morton Hjmand Libor
Market Model LMM
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Q1) Consider a two-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 with two shock terms: \(f ( t + 1 , T ) = f ( t , T ) + \alpha \pm 0.01 \pm 0.01\) ,where the forward rate movements are equiprobable.What this means is that the forward rate may move up by either 0.02 with probability 1/4,or move down by 0.02 with probability 1/4,or remain the same with probability 1/2.What is the price of a put option on a $100 notional,6.5% coupon bond,with a strike price of $100?
A)0.25
B)0.54
C)0.77
D)0.96
Q2) Swap rates in the SMM are,under the risk-neutral forward measure
A)Normal.
B)Lognormal.
C)Exponential.
D)None of the above.
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Page 30
Chapter 29: Credit Derivative Products
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Q1) A credit-sensitive note (CSN)has a coupon that is indexed to the credit rating of the issuer.When the credit rating worsens,CSNs pay a higher rate of interest and when the rating improves they pay a lower rate.Which of the following is the most valid?
A)The risk in these bonds is that they promise to pay a higher coupon when the company's ability to pay is the weakest.
B)The CSN has more risk for the investor than a fixed-coupon bond of the same issuer because the coupons are volatile.
C)Issuers of CSNs prefer to issue these bonds when their ratings are high.
D)CSNs are expensive because they require the issuer to re-rate its bonds more frequently and thereby incur additional costs.
Q2) A digital default swap is a contract that is distinct from a credit default swap in that
A)It pays nothing is no credit event occurs.
B)It pays a fixed amount if a credit event occurs.
C)It has a single premium upfront instead of periodic premium payments.
D)Premium payments are only due if a credit event occurs.
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Chapter 30: Structural Models of Default Risk
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Q1) Altman's Z-score model may be used to:
A)Rank-order firms based on credit quality.
B)Discriminate between firms that are likely to default and those that are not likely to do so.
C)Rate firms.
D)All of the above.
Q2) Credit spreads in the Merton (1974)model will be increasing,ceteris paribus,when
A)Stock volatility decreases.
B)The growth rate of the firm decreases.
C)Leverage increases.
D)The risk-free rates increase.
Q3) Unobserved firm volatility is an obstacle in the implementation of the Merton model.One popular way to overcome this is to
A)Use the model only on non-financial firms.
B)Use equity prices to back out firm volatility.
C)Use equity volatility in place of asset volatility in implementing the model.
D)Use data on closely-related firms from the same sector to infer this volatility.
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Chapter 31: Reduced-Form Models of Default Risk
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Q1) There are two ratings in a very simple world: non-default (ND)and default (D).The real-world rating transition matrix per year is given by: \[P = \left[ \begin{array} { c c } 0.95 & 0.05 \\
0 & 1 \end{array} \right]\] i.e. ,the probability of defaulting when the current state is non-default is 0.05,and a defaulted bond never leaves that state and has zero recovery.The two-year zero-coupon risk-free rate is 4% (continuously-compounded).The price of a default-risk-bearing two-year $100 face value zero-coupon bond is $88.If the off-diagonal one-period transition probabilities in the real-world transition matrix are multiplied by a premium adjustment \[\pi\] to get the risk-neutral transition matrix (as in the Jarrow-Lando-Turnbull model),then given the price of the two-year bond,what is the value of \[\pi\] ?
A)1.97
B)2.00
C)2.03
D)2.10
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Chapter 32: Modeling Correlated Default
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Q1) You are assessing a credit portfolio with 100 issuers where the hazard rate of default of each name is 0.05.The default correlation of all firms (pairwise)is zero.What is the average time it will take for 10% of the portfolio to default?
A)1/5 year
B)1/2 year
C)1 year
D)2 years
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 correlation of default of these two firms closest to?
A)0.25
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