Financial Derivatives
Exam Preparation Guide
Course Introduction
This course provides a comprehensive introduction to financial derivatives, covering fundamental concepts, valuation techniques, and practical applications in risk management. Students will explore derivative instruments such as forwards, futures, options, and swaps, learning how these products are structured and traded in global financial markets. The curriculum emphasizes the pricing of derivatives using models like Black-Scholes and binomial trees and examines hedging strategies employed by financial institutions and corporations. Real-world case studies illustrate the role of derivatives in portfolio management and financial engineering, preparing students to analyze, evaluate, and implement derivative-based solutions to complex financial problems.
Recommended Textbook
Derivatives 2nd Edition by Rangarajan Sundaram
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Chapter 1: Overview
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Q1) Consider hedging an exposure with (i)a futures contract,or (ii)an option with a strike price close to the futures price.The hedge with the futures contract
A)Has more cashflow uncertainty.
B)Has no upfront cost.
C)Has non-negative payoffs.
D)Has more cashflows.
Answer: B
Q2) A US-based exporter anticipated receiving 100 million in six months,and took a short forward position,locking-in an exchange rate of $1.38/ .If after six months,at maturity,the exporter calculates that she has made a profit of $2 million from the hedging strategy,the spot exchange rate at maturity must be
A)$ 0.50/ .
B)$ 1.36/
C)$1.40/
D)$ 2.00/
Answer: B
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3
Chapter 2: Futures Markets
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Q1) Which of the following types of orders does not involve specifying a price limit or trigger price as part of the order?
A)Stop order.
B)Market-if-touched order.
C)A fill-or-kill limit order.
D)A spread order.
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
Q3) Futures contracts are more likely to be cash-settled when
A)The asset underlying the contract is too costly to deliver physically.
B)There is no "underlying" for the futures contract.
C)There are more futures contracts in notional value than the physical stock of the underlying asset.
D)The maturity date of the futures is not the last day of the month.
Answer: A
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Chapter 3: Pricing Forwards and Futures I
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Q1) The presence of the delivery option in a futures contract means that
A)A futures contract may be physically settled but not a forward contract.
B)All else remaining the same,a futures contract will trade at a lower price than a forward.
C)All else remaining the same,a futures contract will trade at a higher price than a forward.
D)A futures contract mat be settled in cash or by delivery of the physical asset.
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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Chapter 4: Pricing Forwards Futures II
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Q1) You are long a forward on the S&P 500 index that you entered into two months ago and has a month left to maturity.If the one-month rate of interest increases,then,ceteris paribus,
A)The value of your forward contract increases.
B)The value of your forward contract decreases.
C)The value of your forward contract is unaffected since the delivery price on your contract was already locked in two months ago.
D)The value of your forward contract is unaffected since the level of the index does not change.
Q2) 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) Suppose you want to hedge a futures contract A with another futures contract B.You calculate the minimum-variance hedge ratio ignoring daily resettlement (for example,by regressing daily changes in Contract A's prices on daily changes in Contract B's prices).Suppose,however,that both contracts are marked-to-market daily.Which of the following statements is always true?
A)The tailed hedge ratio is lower than the untailed one.
B)The tailed hedge ratio is equal to the untailed one.
C)The tailed hedge ratio is greater than the untailed one.
D)None of the above is always true.
Q2) "Basis" risk may arise in a hedging situation if
A)The expiry date of the futures contract and the date on which the hedge is unwound do not coincide.
B)The futures contract used for hedging relates to a commodity that is somewhat different than that being hedged.
C)A disconnect between spot and futures markets causes the failure of the convergence of futures to spot at expiry of the futures contract.
D)All of the above.
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Page 7
Chapter 6: Interest-Rate Forwards Futures
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Q1) Suppose the duration of a bond portfolio is 2.This means
A)The final cash flow from the portfolio will occur in two years.
B)The weighted-average maturity of the portfolio's cash flows is 2 years.
C)The portfolio is fully equivalent to a 2-year zero-coupon bond.
D)The portfolio is fully equivalent to a 2-year par-coupon bond.
Q2) You are short an \(3 \times 6\) FRA and short a eurodollar futures contract expiring in 3 months.Assume the fixed rate in the FRA is the same as the rate locked in via the eurodollar futures contract.If interest rates jump up by 100 basis points,
A)You will lose money on both the FRA and the eurodollar futures.
B)You make money on the FRA but lose on the eurodollar futures.
C)You make money on both the FRA and the eurodollar futures.
D)You lose money on the FRA but make money on the eurodollar futures.
Q3) The payoff of the FRA has the following property
A)It is convex in the Libor rate.
B)It is linear in the Libor rate.
C)It is concave in the Libor rate.
D)None of the above.
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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) Which of the following statements is true of an option's payoff?
A)The gross payoff is always strictly greater than the net payoff.
B)The gross payoff is always strictly less than the net payoff.
C)The gross payoff can be greater or less than than the net payoff.
D)The gross payoff is equal to the net payoff in virtually all cases.
Q3) 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%
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Chapter 8: Options: Payoffs Trading Strategies
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Q1) A stock is currently trading at a price of 22.You observe the following prices for European call options on the stock (the strikes are in parentheses): \(C ( 20 ) = 3.25\) , \(C ( 22 ) = 1.95\) ,and \(C ( 24 ) = 0.40\) .You can conclude from this that
A)The 20-strike call is overvalued.
B)The 24-strike call is undervalued.
C)The prices of the calls are inconsistent with no-arbitrage.
D)The stock is mispriced.
Q2) Consider a position in a long straddle at strike 90 and a short straddle at strike 100,both for the same maturity.which of the following properties is valid for this position?
A)The payoff is increasing in the stock price.
B)The payoff is always positive.
C)The payoff is always negative.
D)The payoff is unbounded.
Q3) In a covered call strategy:
A)The gross payoff is greater than the net payoff.
B)The gross payoff is equal to the net payoff.
C)The gross payoff is smaller than the net payoff.
D)None of the above is always true.
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Chapter 9: No-Arbitrage Restrictions
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Q1) The current price of a stock is $100.The stock pays a dividend of $2 in three months.The risk free rate of interest for all maturities in annualized and continuously-compounded terms is 2%.What is the minimum price of an at-the-money American call option on the stock with six months maturity?
A) \(- \$ 1\)
B)$0
C)$1
D)$2
Q2) Consider two six-month European calls at strikes 90 and 100.The risk free rate is 2%.Which of the following alternatives best describes the condition that must be met by the difference in prices \(C ( 90 ) - C ( 100 )\) ?
A)It must be strictly less than $10.
B)It must be less than or equal to $10.
C)It must be strictly greater than $10.
D)There is insufficient information to answer this question.
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Chapter 10: Early-Exercise/Put-Call Parity
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Q1) The stock price is $50.The strike price of a three-month European put option is $52.If the put option is equal in price to the call option and the stock pays no dividends,then the rate of interest for three month's maturity is
A)4.61%
B)9.23%
C)12.66%
D)15.69%
Q2) 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
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 an investment of a dollar at the risk-free rate returns $1.001668 after one month,and the 98-strike put option is trading at $2,how much arbitrage profit can you make in present value terms?
A)$1.93
B)$2.92
C)$3.93
D)$8.00
Q2) In the binomial model,if the stock moves up by a factor \(\mathcal { U }\) and down by a factor \(d\) ,and a $1 investment in a risk-free bond returns an amount \(R\) per time step,which of the following statements is true in a market that is free from arbitrage?
A) \(d < u < R\)
B) \(u < R < d\)
C) \(d < R < U\)
D) \(R < d < u\)
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13
Chapter 12: Binomial Option Pricing
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Q1) A binomial tree setting has an up-move of \(u > 1\) (with probability \(p = 0.75\) )and a down move of \(d < 1\) (with probability \(1 - p = 0.25\) ),with \(u - 1 = 1 - d\)
.The risk-free interest rate per time step is zero,so a dollar invested at the beginning of the period returns \(R = \$ 1\) at the end of the period.The risk-neutral probability of an up-move in this setting
A)Is \(> \frac { 1 } { 2 }\) )
B)Is \(< \frac { 1 } { 2 }\)
C)Is equal to \(\frac { 1 } { 2 }\)
D)Is equal to \(p\)
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) 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 expected simple return on the stock for one month?
A)0.83
B)1.01
C)1.08
D)1.13
Q2) Let \(S _ { T }\) denote the time- \(T\) price of a stock and \(S _ { 0 }\) its current price.Suppose that for any \(T\) , \(\ln \left( \frac { S _ { T } } { S _ { 0 } } \right) : N
\left( \mu _ { T } , \sigma ^ { 2 } T \right)\) for constant annual parameters \(\mu\) and \(\sigma\) .What does this imply about the returns process? Pick the most accurate of the following alternatives:
A)The returns are independent and identically distributed over time.
B)The returns are independent over time.
C)The returns are normally distributed.
D)None of the above.
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Page 15
Chapter 14: The Black-Scholes Model
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Q1) Consider a Black-Scholes setting.When a call option is deep in-the-money,an increase in volatility results in,ceteris paribus,
A)A decrease in the delta of the option.
B)A decrease in the insurance value of the option.
C)An increase in the intrinsic value of the option.
D)An increase in the time value of the option.
Q2) A volatility swap is an option on the realized standard deviation of a stock's return over a defined period of time.A volatility swap may be replicated using
A)A static position in forwards and options on the stock.
B)A static position in stock,forwards and options.
C)A dynamic position in forwards and options on the stock.
D)None of the above
Q3) The implied volatility skew observed in stock indices cannot be attributed to which of the following reasons?
A)The distribution of index returns is non-normal.
B)The skewness of index returns is much greater than zero.
C)The excess kurtosis of index returns is much greater than zero.
D)There is crash risk in the index.
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Chapter 15: Mathematics of Black-Scholes
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Q1) Option pricing in continuous time makes use of Wiener processes.Which of the following is not a property of a Wiener process \(W _ { t }\) ,given \(W _ { 0 } = 0\) ?
A)The process has independent increments \(W _ { t } - W _ { s }\) ,for \(t > s\)
)
B)Increments are normally distributed.
C)For each \(\pm\)
, \(W _ { t }\)
Is normally distributed with mean zero and variance \(t ^ { 2 }\) )
D)The process \(\left( W _ { t } \right)\) Is a symmetric random walk around zero.
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Chapter 16: Beyond Black-Scholes
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Q1) For the same problem in the preceding two questions,find the state price at the middle node after two periods,given that the 117.3008--strike call is priced at $4 and the 85.2509--strike put is priced at $4,both options of two-months maturity.Assume that the middle node after two periods has the same stock price as the initial stock price.
A)0.5016
B)0.5023
C)0.5044
D)0.5117
Q2) 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
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Page 18
Chapter 17: The Option Greeks
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Q1) You hold a portfolio of a long position in a call and a long position in a put,both for the same strike and maturity.Which of the following statements is true?
A)When the stock price increases,the delta of the portfolio increases if the call is in-the-money.
B)When the stock price increases,the delta of the portfolio decreases if the call is out-of-the-money.
C)When the stock price increases,the delta of the portfolio increases whether or not the call is in-the-money.
D)There is not enough information to answer this question.
Q2) The delta of a call option is 0.6.The current price of the call is $5 and that of a put at the same strike is $4,and the stock is at $100.What is the approximate price of the put if the stock price increases to $100.50?
A)$3.60
B)$3.80
C)$4.20
D)$4.50
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Chapter 18: Path-Independent Exotic Options
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Q1) A cash-or-nothing call option written on a stock
A)Pays the value of the stock in cash if the option finishes in-the-money and nothing otherwise.
B)Pays a fixed amount of cash if the option finishes in-the-money and nothing otherwise.
C)Is any cash-settled standard call option.
D)Pays the difference between the stock price and strike price in cash to the option holder if the option should finish in-the-money and nothing otherwise.
Q2) The gamma of a cash-or-nothing binary call option is generally when the option is out-of-the-money and generally when it is in-the-money.
A)negative;positive.
B)negative;negative.
C)positive;negative.
D)positive;positive.
Q3) The delta of a cash-or-nothing call option is highest when the option is
A)Deep out-of-the-money.
B)At- or near-the-money.
C)Deep in-the-money.
D)25% out-of-the-money.
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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) When is an Asian option less useful than a vanilla option?
A)For reducing the incentives for price manipulation of the underlying close to maturity.
B)For making the option less sensitive to jump risk close to maturity.
C)For hedging exposure to the average price of a security.
D)For taking directional bets.
Q3) When volatility increases,the value of a down-and-out put ,and the value of a down-and-in put.
A)increases;increases.
B)decreases;increases.
C)may increase or decrease;increases.
D)decreases;may increase or decrease.
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21
Chapter 20: Value at Risk
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Q1) The delta-normal method for computing VaR has many advantages.Which of the following is not a characteristic of the delta-normal approach?
A)VaR can be calculated analytically.
B)It is simple to apply because it uses the normal probability distribution.
C)It is a non-parametric method.
D)It can be used to compute risk-decompositions.
Q2) You invest $100 each in two bonds.Each bond will pay you $110 at the end of the year with probability 0.98 and nothing with probability 0.02.The correlation between the bonds is zero.In this scenario,the 95%-VaR of your portfolio is
A) \(- 20\)
)
B)Zero.
C)$90
D)$200
Q3) VaR fails the following requirement of a "coherent" risk measure:
A)Linear homogeneity.
B)Monotonicity.
C)Subadditivity.
D)Translation invariance.
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Page 22
Chapter 21: Swaps and Floating Rate Products
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Q1) The UK money-market day-count convention is
A)Actual/365.
B)Actual/360.
C)Actual/Actual.
D)30/360.
Q2) A bank makes long-term fixed-rate loans,and funds itself with short-term deposits.It can best manage its vulnerability to interest rate changes by
A)Entering into a basis (floating-floating)swap.
B)Entering into a pay-floating/receive-fixed interest rate swap.
C)Entering into a pay-fixed/receive-floating interest rate swap.
D)Entering into a fixed-fixed swap where the two legs have different payment frequencies.
Q3) Who is likely to bear the greater counterparty risk in a swap where A pays fixed and B pays floating if interest rates are expected to rise over the life of the swap?
A)a.
B)b.
C)Both A and B.
D)There is not enough information to determine the correct answer.
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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 $100 notional equity-for-equity swap on two stocks where the price of the stocks at inception was $40 and $50,respectively.At the present time,sixty-one days after inception,the two stock prices are $39 and $51,respectively.If you pay the return on the first stock and receive the return on the second stock,what is your valuation of the equity swap after sixty-one days? Assume that the Libor interest rate on an ACT/360 basis from now till the next settlement date is 10% for the remaining 122 days.
A) \(- \$ 2.00\)
B)Zero
C) \(+ \$ 4.35\)
D) \(+ \$ 4.50\)
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Page 24
Chapter 23: Currency and Commodity Swaps
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Q1) You are a CFO of a major corporation,and want to buy dollars in exchange for euros.The bank quotes you the following currency rate ($/ ): 1.50-1.52.At what rate will you buy?
A)1.50
B)1.51
C)1.52
D)Insufficient information to answer this question.
Q2) Consider an oil swap in which you pay the floating price of oil in exchange for a fixed amount \(A\) .The price of a new oil swap (i.e. ,the breakeven value \(A\) )increases when
A)The spot price of the commodity declines.
B)The convenience yield on the commodity increases.
C)Interest rates rise.
D)All of the above.
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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) If the ytm of a bond falls,which of the following is most valid?
A)The bond price rises.
B)The bond price falls.
C)The bond price may rise or fall,depending on the maturity of the bond.
D)Not enough information to answer the question.
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,at least what must the product be for money to triple?
A)90
B)100
C)110
D)120
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Chapter 25: Estimating the Yield Curve
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Q1) A major advantage of the cubic spline approach is that it can be estimated using ordinary least squares (OLS)regression.Which of the following is NOT related to this estimation feature?
A)OLS may be used because the price of bonds is the just the product of cashflows and discount functions summed up over all cash flows.
B)OLS enables the use of all the bonds in the data set,even though there are more bonds than parameters to be estimated.
C)OLS works for polynomials of any order in the splining function.
D)OLS may be used because it satisfies the smoothness condition required for the forward curve in the estimation.
Q2) The Nelson-Siegel-Svensson model is
A)A special kind of splining technique.
B)Adds an exponential spline to the Nelson-Siegel model.
C)An alternative approach to splines in estimating yield curves.
D)A superior approach to splines in estimating the yield curve.
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Chapter 26: Modeling Term Structure Movements
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Q1) "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
Q2) 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.
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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 put option on a 7.5% coupon (annual pay)bond at a strike of $100 (ex-coupon)?
A)1.00
B)1.08
C)1.16
D)1.24
Q2) In the Black-Derman-Toy (BDT)model,short rates have
A)Constant volatility for all maturities.
B)Volatility that changes by maturity of the short rate.
C)Volatility that varies by maturity and level of the short rate,i.e. ,state-dependent volatility.
D)Stochastic volatility.
Q3) An exponential-affine short rate bond model is one
A)That most bond traders have an affinity for.
B)Where the bond prices are linear in the short-rate.
C)Where the logarithm of bond prices is linear in the short rate.
D)Where the bond price is based on discrete compounding.
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Chapter 28: The Heath-Jarrow-Morton Hjmand Libor
Market Model LMM
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Q1) The numeraire in the Swap Market Model (SMM)is
A)The price of the longest maturity bond (i.e. ,the numeraire under forward measure).
B)The total of discount functions to the longest swap maturity.
C)The money market account.
D)The value of the fixed side of the swap.
Q2) In the HJM model,one of the striking features is that the risk-neutral drifts in the model are functions of only the
A)The forward rates.
B)The yields.
C)The volatility of forward rates.
D)The risk premia for interest-rate risk.
Q3) The Libor Market Model is most often implemented by means of A)A binomial tree.
B)A trinomial tree.
C)Monte Carlo simulation.
D)A closed-form approximation equation for derivative prices.
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Page 30
Chapter 29: Credit Derivative Products
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Q1) Credit risk in bonds involves uncertainty about whether the bond will default (default risk),and uncertainty about the value of the bonds when they default (recovery risk).In order to profit from a view that default risk will worsen,while not taking a view on recovery risk,you would most prefer to
A)Buy a credit default swap (CDS)and sell a digital default swap (DDS).
B)Sell a credit default swap (CDS)and buy a digital default swap (DDS).
C)Sell a credit default swap (CDS).
D)Buy a digital default swap (DDS).
Q2) CDS settlement is not likely to be triggered by which of the following events?
A)A restructuring of the company.
B)A secondary equity offering by the company.
C)Failure to make interest payments on bonds of the company.
D)The company repudiates its debt.
Q3) Which of the following credit derivatives is not a pure credit risk instrument,i.e. ,is a bet on more than just credit risk?
A)Credit spread forwards.
B)Credit spread options.
C)Total return swap.
D)Credit default swap.
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Page 31
Chapter 30: Structural Models of Default Risk
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Q1) 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%
Q2) A firm's current value is \(£\) 1 billion .The firm has one-year zero-coupon debt outstanding with a face value of \(£\) 0.6 billion.What is the one-year "distance to default" (in the Moody's KMV approach)if the standard deviation of firm value is 30%?
A)1.33
B)1.71
C)2.34
D)3.12
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Chapter 31: Reduced-Form Models of Default Risk
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Q1) 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
Q2) Empirically,recessions witness a rise in default rates.Which of the following scenarios also accompanies the rise in default rates?
A)Recovery rates rise.
B)Loss given default (LGD)falls
C)LGD rises
D)LGD becomes highly volatile.
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33
Chapter 32: Modeling Correlated Default
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Q1) Consider two firms with one-year probabilities of default of \[p _ { 1 } = 0.10\] and \[p _ { 2 } = 0.05\] ,respectively.The correlation of default of these two firms is \[\rho = 0.30\] .What is the probability that both firms default in one year?
A)1.0%
B)1.5%
C)2.0$
D)2.5%
Q2) Consider two firms with one-year probabilities of default of \[p _ { 1 } = 0.10\] and \[p _ { 2 } = 0.05\] ,respectively.The correlation of default of these two firms is \[\rho = 0.30\] .What is the price of a $100 notional one-year maturity second-to-default basket option on these two firms? (Assume the discount rate is zero. )
A)$2.50
B)$5.50
C)$11.25
D)$17.75
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