Derivatives Markets Solved
Exam Questions
Course Introduction
This course provides an in-depth exploration of derivatives markets, focusing on the trading, valuation, and risk management of financial instruments such as forwards, futures, options, and swaps. Students will examine the structure and functioning of derivatives exchanges, the roles of various market participants, and the economic rationale behind derivative instruments. Topics include pricing models, hedging strategies, regulatory frameworks, and the application of derivatives in financial engineering. Real-world case studies and practical exercises equip students with the skills necessary to analyze and use derivatives effectively in both investment and risk management contexts.
Recommended Textbook
Fundamentals of Futures and Options Markets 9th Edition by John C. Hull
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Chapter 1: Introduction
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Q1) Which of the following is NOT true
A) When a CBOE call option on IBM is exercised, IBM issues more stock
B) An American option can be exercised at any time during its life
C) An call option will always be exercised at maturity if the underlying asset price is greater than the strike price
D) A put option will always be exercised at maturity if the strike price is greater than the underlying asset price.
Answer: A
Q2) A trader has a portfolio worth $5 million that mirrors the performance of a stock index. The stock index is currently 1,250. Futures contract trade on the index with one contract being on 250 times the index. To remove market risk from the portfolio the trader should
A) Buy 16 contracts
B) Sell 16 contracts
C) Buy 20 contracts
D) Sell 20 contracts
Answer: B
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Chapter 2: Futures Markets and Central Counterparties
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Q1) One futures contract is traded where both the long and short parties are closing out existing positions. What is the resultant change in the open interest?
A) No change
B) Decrease by one
C) Decrease by two
D) Increase by one
Answer: B
Q2) Margin accounts have the effect of
A) Reducing the risk of one party regretting the deal and backing out
B) Ensuring funds are available to pay traders when they make a profit
C) Reducing systemic risk due to collapse of futures markets
D) All of the above
Answer: D
Q3) Who initiates delivery in a corn futures contract
A) The party with the long position
B) The party with the short position
C) Either party
D) The exchange
Answer: B
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Page 4
Chapter 3: Hedging Strategies Using Futures
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Q1) Which of the following describes tailing the hedge?
A) A strategy where the hedge position is increased at the end of the life of the hedge
B) A strategy where the hedge position is increased at the end of the life of the futures contract
C) A more exact calculation of the hedge ratio when forward contracts are used for hedging
D) None of the above
Answer: D
Q2) Which of the following best describes "stack and roll"?
A) Creates long-term hedges from short term futures contracts
B) Can avoid losses on futures contracts by entering into further futures contracts
C) Involves buying a futures contract with one maturity and selling a futures contract with a different maturity
D) Involves two different exposures simultaneously
Answer: A
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Chapter 4: Interest Rates
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Q1) Which of the following is true?
A) When interest rates in the economy increase, all bond prices increase
B) As its coupon increases, a bond's price decreases
C) Longer maturity bonds are always worth more that shorter maturity bonds when the coupon rates are the same
D) None of the above
Q2) Bootstrapping involves
A) Calculating the yield on a bond
B) Working from short maturity instruments to longer maturity instruments determining zero rates at each step
C) Working from long maturity instruments to shorter maturity instruments determining zero rates at each step
D) The calculation of par yields
Q3) Which of the following is true of LIBOR
A) The LIBOR rate is free of credit risk
B) A LIBOR rate is lower than the Treasury rate when the two have the same maturity
C) It is a rate used when borrowing and lending takes place between banks
D) It is subject to favorable tax treatment in the U.S.
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Chapter 5: Determination of Forward and Futures Prices
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Q1) An exchange rate is 0.7000 and the six-month domestic and foreign risk-free interest rates are 5% and 7% (both expressed with continuous compounding). What is the six-month forward rate?
A) 0.7070
B) 0.7177
C) 0.7249
D) 0.6930
Q2) Which of the following is a consumption asset?
A) The S&P 500 index
B) The Canadian dollar
C) Copper
D) IBM stock
Q3) Which of the following is true?
A) The convenience yield is always positive or zero.
B) The convenience yield is always positive for an investment asset.
C) The convenience yield is always negative for a consumption asset.
D) The convenience yield measures the average return earned by holding futures contracts.
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7
Chapter 6: Interest Rate Futures
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Q1) A company invests $1,000 in a five-year zero-coupon bond and $4,000 in a ten-year zero-coupon bond. What is the duration of the portfolio?
A) 6 years
B) 7 years
C) 8 years
D) 9 years
Q2) Which of the following is NOT an option open to the party with a short position in the Treasury bond futures contract?
A) The ability to deliver any of a number of different bonds
B) The wild card play
C) The fact that delivery can be made any time during the delivery month
D) The interest rate used in the calculation of the conversion factor
Q3) Which of the following is closest to the duration of a 2-year bond that pays a coupon of 8% per annum semiannually? The yield on the bond is 10% per annum with continuous compounding.
A) 1.82
B) 1.85
C) 1.88
D) 1.92
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Page 8
Chapter 7: Swaps
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Q1) A company enters into an interest rate swap where it is paying fixed and receiving LIBOR. When interest rates increase, which of the following is true?
A) The value of the swap to the company increases
B) The value of the swap to the company decreases
C) The value of the swap can either increase or decrease
D) The value of the swap does not change providing the swap rate remains the same
Q2) Which of the following is a use of a currency swap?
A) To exchange an investment in one currency for an investment in another currency
B) To exchange borrowing in one currency for borrowings in another currency
C) To take advantage situations where the tax rates in two countries are different
D) All of the above
Q3) Which of the following describes an interest rate swap?
A) A way of converting a liability from fixed to floating
B) A portfolio of forward rate agreements
C) An agreement to exchange interest at a fixed rate for interest at a floating rate
D) All of the above
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Chapter 8: Securitization and the Credit Crisis of 2007
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Q1) Which of the following were introduced before the credit crisis that started in 2007
A) Basel II
B) Dodd-Frank
C) Basel III
D) Requirements for living wills
Q2) Suppose that ABSs are created from portfolios of subprime mortgages with the following allocation of the principal to tranches: senior 85%, mezzanine 10%, and equity 5%. (The portfolios of subprime mortgages have the same default rates.) An ABS CDO is then created from the mezzanine tranches with the same allocation of principal. How high can losses on the mortgages be before the mezzanine tranche of the ABD CDO bears losses?
A) 5.0%
B) 5.5%
C) 6.0%
D) 6.5%
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Chapter 9: Mechanics of Options Markets
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Q1) Which of the following are true for CBOE stock options?
A) There are no margin requirements
B) The initial margin and maintenance margin are determined by formulas and are equal
C) The initial margin and maintenance margin are determined by formulas and are different
D) The maintenance margin is usually about 75% of the initial margin
Q2) The price of a stock is $67. A trader sells 5 put option contracts on the stock with a strike price of $70 when the option price is $4. The options are exercised when the stock price is $69. What is the trader's net profit or loss?
A) Loss of $1,500
B) Loss of $500
C) Gain of $1,500
D) Loss of $1,000
Q3) Which of the following describes a long position in an option?
A) A position where there is more than one year to maturity
B) A position where there is more than five years to maturity
C) A position where an option has been purchased
D) A position that has been held for a long time
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Page 11
Chapter 10: Properties of Stock Options
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Q1) Which of the following best describes the intrinsic value of an option?
A) The value it would have if the owner were forced to exercise immediately
B) The Black-Scholes-Merton price of the option
C) The lower bound for the option's price
D) The amount paid for the option
Q2) Which of the following is true?
A) An American call option on a stock should never be exercised early
B) An American call option on a stock should never be exercised early when no dividends are expected
C) There is always some chance that an American call option on a stock will be exercised early
D) There is always some chance that an American call option on a stock will be exercised early when no dividends are expected
Q3) When the strike price increases with all else remaining the same, which of the following is true?
A) Both calls and puts increase in value
B) Both calls and puts decrease in value
C) Calls increase in value while puts decrease in value
D) Puts increase in value while calls decrease in value
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Page 12
Chapter 11: Trading Strategies Involving Options
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Q1) Which of the following describes a protective put?
A) A long put option on a stock plus a long position in the stock
B) A long put option on a stock plus a short position in the stock
C) A short put option on a stock plus a short call option on the stock
D) A short put option on a stock plus a long position in the stock
Q2) Six-month call options with strike prices of $35 and $40 cost $6 and $4, respectively. What is the maximum gain when a bull spread is created by trading a total of 200 options?
A) $100
B) $200
C) $300
D) $400
Q3) How can a straddle be created?
A) Buy one call and one put with the same strike price and same expiration date
B) Buy one call and one put with different strike prices and same expiration date
C) Buy one call and two puts with the same strike price and expiration date
D) Buy two calls and one put with the same strike price and expiration date
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Chapter 12: Introduction to Binomial Trees
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Q1) The current price of a non-dividend paying stock is $50. Use a two-step tree to value an American put option on the stock with a strike price of $48 that expires in 12 months. Each step is 6 months, the risk free rate is 5% per annum, and the volatility is 20%. Which of the following is the option price?
A) $1.95
B) $2.00
C) $2.05
D) $2.10
Q2) In a binomial tree created to value an option on a stock, the expected return on stock is
A) Zero
B) The return required by the market
C) The risk-free rate
D) It is impossible to know without more information
Q3) Which of the following is NOT true in a risk-neutral world?
A) The expected return on a call option is independent of its strike price
B) Investors expect higher returns to compensate for higher risk
C) The expected return on a stock is the risk-free rate
D) The discount rate used for the expected payoff on an option is the risk-free rate
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Page 14
Chapter 13: Valuing Stock Options: the Bsm Model
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Q1) A stock price is $100. Volatility is estimated to be 20% per year. What is an estimate of the standard deviation of the change in the stock price in one week?
A) $0.38
B) $2.77
C) $3.02
D) $0.76
Q2) Which of the following is true when there are dividends
A) It is never optimal to exercise a call option on the stock early
B) It can be optimal to exercise a call option at any time
C) It is only ever optimal to exercise a call option immediately after an ex-dividend date
D) None of the above
Q3) The volatility of a stock is 18% per year. What is the volatility per month?
A) 1.5%
B) 3.0%
C) 5.2%
D) None of the above
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15
Chapter 14: Employee Stock Options
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Q1) Which of the following ensures that managers are rewarded only when a company performs better than its competitors?
A) A constant strike price for executive stock options
B) A strike price that increases with time
C) A strike price that changes in line with an index of stock prices
D) A strike price that is tied to reported profit
Q2) Which of the following is true?
A) An employee stock option is usually held to maturity
B) An employee stock option tends to be exercised earlier than an OTC option with the same terms
C) An employee stock options tends to be exercised later than an OTC option with the same terms
D) Employee stock options are usually exercised as early as possible
Q3) Which of the following is NOT usually true about employee stock options?
A) There is a vesting period
B) They can be sold to other employees
C) They are often at-the-money when issued
D) Their value is currently a charge to the income statement
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Chapter 15: Options on Stock Indices and Currencies
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Q1) A portfolio manager in charge of a portfolio worth $10 million is concerned that the market might decline rapidly during the next six months and would like to use options on an index to provide protection against the portfolio falling below $9.5 million. The index is currently standing at 500 and each contract is on 100 times the index. What should the strike price of options on the index be the portfolio has a beta of 0.5? Assume that the risk-free rate is 10% per annum and the dividend yield on both the portfolio and the index is 2% per annum.
A) 400
B) 410
C) 420
D) 430
Q2) A binomial tree with three-month time steps is used to value a currency option. The domestic and foreign risk-free rates are 4% and 6% respectively. The volatility of the exchange rate is 12%. What is the probability of an up movement?
A) 0.4435
B) 0.5267
C) 0.5565
D) 0.5771
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Page 17
Chapter 16: Futures Options and Blacks Model
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Q1) What is the growth rate of an index futures price in the risk-neutral world?
A) The excess of the risk-free rate over the dividend yield
B) The risk-free rate
C) The dividend yield on the index
D) Zero
Q2) What is the cash settlement if a call futures option on 50 units of the underlying asset is exercised?
A) (Current Futures Price - Strike Price) times 50
B) (Strike Price - Current Futures Price) times 50
C) (Most Recent Futures Settlement Price - Strike Price) times 50
D) (Strike Price - Most Recent Futures Settlement Price) times 50
Q3) Which of the following is true when the futures price exceeds the spot price?
A) Calls on futures should never be exercised early
B) Put on futures should never be exercised early
C) A call on futures is always worth at least as much as the corresponding call on spot
D) A call on spot is always worth at least as much as the corresponding call on futures
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18
Chapter 17: The Greek Letters
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Q1) A trader uses a stop-loss strategy to hedge a short position in a three-month call option with a strike price of 0.7000 on an exchange rate. The current exchange rate is 0.6950 and value of the option is 0.1. The trader covers the option when the exchange rate reaches 0.7005 and uncovers (i.e., assumes a naked position) if the exchange rate falls to 0.6995. Which of the following is NOT true?
A) The exchange rate trading might cost nothing so that the trader gains 0.1 for each option sold
B) The exchange rate trading might cost considerably more than 0.1 for each option sold so that the trader loses money
C) The present value of the gain or loss from the exchange rate trading should be about 0.1 on average for each option sold
D) The hedge works reasonably well
Q2) Gamma tends to be high for which of the following
A) At-the money options
B) Out-of-the money options
C) In-the-money options
D) Options with a long time to maturity
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Page 19
Chapter 18: Binomial Trees in Practice
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Q1) For an option on futures, the volatility is 35%, the time step is three months, and the risk-free rate is 5%. What is the Cox, Ross, Rubinstein parameter, u?
A) 1.34
B) 1.29
C) 1.09
D) 1.19
Q2) Which of the following is true for u in a Cox-Ross-Rubinstein binomial tree?
A) It depends on the interest rate and the volatility
B) It depends on the volatility but not the interest rate
C) It depends on the interest rate but not the volatility
D) It depends on neither the interest rate nor the volatility
Q3) When we move from assuming no dividends to assuming a constant dividend yield, which of the following is true for a Cox, Ross, Rubinstein tree?
A) The parameters u and p change
B) p changes but u does not
C) u changes but p does not
D) Neither p nor u changes
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Chapter 19: Volatility Smiles
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Q1) If the volatility implied from an at-the-money put currency option were used to price other put options on the currency, which of the following would be true?
A) Out-of-the money and in-the-money prices would be too high
B) Out-of-the money and in-the-money prices would be too low
C) Out-of-the-money option prices would be too high and in-the-money option prices would be too low
D) Out-of-the-money option prices would be too low and in-the-money option prices would be too high
Q2) Which of the following could cause the volatility smile typically seen for foreign currency options?
A) Currencies are traded in different countries at different times of the day
B) Currencies tend to have low volatilities
C) The activities of central banks causes occasional jumps in the exchange rate
D) Interest rates may be different in the two countries
Q3) Which of the following is true?
A) Volatility smile for European puts is the same as for European calls
B) Volatility smile for European puts is the same as for American puts
C) Volatility smile for European calls is the same as for American calls
D) Volatility smile for American puts is the same as for American calls
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Page 21
Chapter 20: Value at Risk and Expected Shortfall
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Q1) At the end of Thursday, the estimated covariance between assets A and B is 0.0001. During Friday asset A produces a return of 3% and asset B produces a return of zero. An EWMA model with lambda equal to 0.9 is used. What is an estimate of the covariance at the end of Friday?
A) 0.000090
B) 0.000081
C) 0.000100
D) 0.000095
Q2) Which of the following is true when delta, but not gamma, is used in calculating VaR for option positions?
A) VaR for a long call is too low and VaR for a long put is too low
B) VaR for a long call is too low and VaR for a long put is too high
C) VaR for a long call is too high and VaR for a long put is too low
D) VaR for a long call is too high and VaR for a long put is too high
Q3) Which of the following is true of the 99.9% value at risk?
A) There is 1 chance in 10 that the loss will be greater than the value of risk
B) There is 1 chance in 100 that the loss will be greater than the value of risk
C) There is 1 chance in 1000 that the loss will be greater than the value of risk
D) None of the above
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Page 22
Chapter 21: Interest Rate Options
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Q1) Which of the following is an implication of the mean reversion of interest rates?
A) Interest rates cannot become negative
B) When short-term interest rates are high they tend to move down
C) The term structure of interest rates tends to be upward sloping
D) When short-term interest rates are low they tend to stay low
Q2) What is exchanged when a put option on an interest rate futures is exercised?
A) A long position in a futures contract for the holder of the option and a short position in a futures contract for the option writer
B) A short position in a futures contract for the holder of the option and a long position in a futures contract for the option writer
C) Cash payoff, a long position in a futures contract for the holder of the option, and a short position in a futures contract for the option writer
D) Cash payoff, a short position in a futures contract for the holder of the option, and a long position in a futures contract for the option writer
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Chapter 22: Exotic Options and Other Nonstandard Products
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Q1) When can Bermudan options be exercised?
A) Any time during the life of the options
B) Any time after a certain date up to the end of the life of the life
C) Any time before a certain date or at the end of the option's life
D) On dates specified at the start of the option
Q2) Which of the following describes a cliquet option
A) An option to exchange one asset for another
B) An instrument when the holder can choose between several alternative options
C) An option on an option with predetermined strike prices for the two options
D) A series of options with rules for determining strike prices
Q3) In a shout call option the strike price is $30. The holder shouts when the asset price is $40. What is the payoff from the option if the final asset price is $35?
A) $0
B) $5
C) $10
D) $15
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Chapter 23: Credit Derivatives
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Q1) A hazard rate is 1% per annum. What is the probability of a default during the first two years?
A) 2.00%
B) 2.02%
C) 1.98%
D) 1.96%
Q2) Which of the following is true about a CDS?
A) Restructuring is never a credit event
B) Restructuring is always a credit event
C) Certain types of restructuring qualify as credit events but others do not
D) Sometimes a CDS is defined so that restructuring is a credit event and sometimes it is not
Q3) Which of the following is the most popular life for a credit default swap?
A) 1 year
B) 3 years
C) 5 years
D) 10 years
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25
Chapter 24: Weather, Energy, and Insurance Derivatives
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Q1) Which of the following are least likely to use weather derivatives?
A) Energy producers
B) Food and drink manufacturers
C) Companies in the leisure industry
D) Automobile manufacturers
Q2) Which of the following describes a CAT bond?
A) Has a great deal of systematic risk
B) Has very little systematic risk
C) Has a moderate amount of systematic risk
D) Has negative systematic risk
Q3) Which of the following describes a typical reinsurance contract?
A) Covers a percentage of all losses by an insurance company
B) Covers all losses of the insurance company up to a certain amount
C) Covers all losses of the insurance company above a certain amount
D) Covers all losses of the insurance company between two amounts
Q4) Which of the following is the basis for calculating HDD and CDD?
A) The average temperature during the day
B) The average of the highest and lowest temperature during the day
C) The temperature at 12 noon during the day
D) None of the above
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