Options and Futures
Exam Solutions
Course Introduction
This course provides a comprehensive introduction to options and futures markets, emphasizing their role in modern financial systems. Students will explore the fundamental characteristics and valuation of derivatives such as options, futures, and swaps, and learn how these instruments can be used for hedging, speculation, and risk management. The course covers pricing models, trading strategies, and the impact of market variables on derivative values, with a balance of theoretical concepts and practical applications. Through real-world case studies and problem-solving exercises, participants will develop the analytical skills necessary to understand and navigate the complexities of derivatives markets.
Recommended Textbook
Options Futures and Other Derivatives 9th Edition by John
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2
C. Hull
Chapter 1: Introduction
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Q1) A speculator can choose between buying 100 shares of a stock for $40 per share and buying 1000 European call options on the stock with a strike price of $45 for $4 per option.For second alternative to give a better outcome at the option maturity,the stock price must be above
A)$45
B)$46
C)$55
D)$50
Answer: D
Q2) Which of the following is NOT true about call and put options:
A)An American option can be exercised at any time during its life
B)A European option can only be exercised only on the maturity date
C)Investors must pay an upfront price (the option premium) for an option contract
D)The price of a call option increases as the strike price increases
Answer: D
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Chapter 2: Mechanics of Futures Markets
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Q1) With bilateral clearing,the number of agreements between four dealers,who trade with each other, is
A)12
B)1
C)6
D)2
Answer: C
Q2) You sell one December futures contracts when the futures price is $1,010 per unit.Each contract is on 100 units and the initial margin per contract that you provide is $2,000.The maintenance margin per contract is $1,500.During the next day the futures price rises to $1,012 per unit.What is the balance of your margin account at the end of the day?
A)$1,800
B)$3,300
C)$2,200
D)$3,700
Answer: B
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Chapter 3: Hedging Strategies Using Futures
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Q1) On March 1 the price of a commodity is $1,000 and the December futures price is $1,015.On November 1 the price is $980 and the December futures price is $981.A producer of the commodity entered into a December futures contracts on March 1 to hedge the sale of the commodity on November 1.It closed out its position on November 1.What is the effective price (after taking account of hedging)received by the company for the commodity?
A)$1,016
B)$1,001
C) $981
D) $1,014
Answer: D
Q2) Which of the following is necessary for tailing a hedge?
A)Comparing the size in units of the position being hedged with the size in units of the futures contract
B)Comparing the value of the position being hedged with the value of one futures contract
C)Comparing the futures price of the asset being hedged to its forward price
D)None of the above
Answer: B
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Page 5
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) The two-year zero rate is 6% and the three year zero rate is 6.5%.What is the forward rate for the third year? All rates are continuously compounded.
A)6.75%
B)7.0%
C)7.25%
D)7.5%
Q3) The compounding frequency for an interest rate defines
A)The frequency with which interest is paid
B)A unit of measurement for the interest rate
C)The relationship between the annual interest rate and the monthly interest rate
D)None of the above
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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 NOT true?
A)Gold and silver are investment assets
B)Investment assets are held by significant numbers of investors for investment purposes
C)Investment assets are never held for consumption
D)The forward price of an investment asset can be obtained from the spot price, interest rates, and the income paid on the asset
Q3) Which of the following is a consumption asset?
A)The S&P 500 index
B)The Canadian dollar
C)Copper
D)IBM stock
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Page 7
Chapter 6: Interest Rate Futures
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Q1) Which of the following is NOT true about duration?
A)It equals the years-to-maturity for a zero coupon bond
B)It equals the weighted average of payment times for a bond, where weights are proportional to the present value of payments
C)Equals the weighted average of individual bond durations for a portfolio, where weights are proportional to the present value of bond prices
D)The prices of two bonds with the same duration change by the same percentage amount when interest rate moves up by 100 basis points
Q2) Which of the following day count conventions applies to a US Treasury bond?
A)Actual/360
B)Actual/Actual (in period)
C)30/360
D)Actual/365
Q3) Duration matching immunizes a portfolio against
A)Any parallel shift in the yield curve
B)All shifts in the yield curve
C)Changes in the steepness of the yield curve
D)Small parallel shifts in the yield curve
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Chapter 7: Swaps
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Q1) Which of the following is true for an interest rate swap?
A)A swap is usually worth close to zero when it is first negotiated
B)Each forward rate agreement underlying a swap is worth close to zero when the swap is first entered into
C)Comparative advantage is a valid reason for entering into the swap
D)None of the above
Q2) Which of the following describes the way a LIBOR-in-arrears swap differs from a plain vanilla interest rate swap?
A)Interest is paid at the beginning of the accrual period in a LIBOR-in-arrears swap
B)Interest is paid at the end of the accrual period in a LIBOR-in-arrears swap
C)No floating interest is paid until the end of the life of the swap in a LIBOR-in-arrears swap, but fixed payments are made throughout the life of the swap
D)Neither floating nor fixed payments are made until the end of the life of the swap
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Chapter 8: Securitization and the Credit Crisis of 2007
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Q1) AIG lost money because
A)It bought tranches created from mortgages
B)It invested heavily in real estate
C)It invested heavily in the stock market
D)It insured AAA tranches of ABS CDOs
Q2) How high can losses on the mortgages be before the senior tranche of the ABS CDO bears losses?
A)5.5%
B)6.0%
C)6.5%
D)7.0%
Q3) Which of the following is NOT true
A)The bonus structure at banks can lead to short-term horizons for decision making
B)Securitization involves the transfer of risk
C)The term "agency costs" describes the situation where the incentives of two parties in a business relationship are not perfectly aligned
D)Correlations decrease in stressed market conditions
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Chapter 9: OIS Discounting, Credit Issues, and Funding Costs
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Q1) Since the 2008 credit crisis
A)LIBOR has replaced OIS as the discount rate for non-collateralized swaps
B)OIS has replaced LIBOR as the discount rate for non-collateralized swaps
C)LIBOR has replaced OIS as the discount rate for collateralized swaps
D)OIS has replaced LIBOR as the discount rate for collateralized swaps
Q2) Accountants like to value a derivatives portfolio at
A)The bid price
B)The offer price
C)The exit price
D)Original cost less depreciation
Q3) Since the credit crisis that started in 2007 which of the following have derivatives traders used as the risk-free discount rate for collateralized transactions
A)The Treasury rate
B)The LIBOR rate
C)The repo rate
D)The overnight indexed swap rate
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11
Chapter 10: Mechanics of Options Markets
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Q1) In which of the following cases is an asset NOT considered constructively sold?
A)The owner shorts the asset
B)The owner buys an in-the-money put option on the asset
C)The owner shorts a forward contract on the asset
D)The owner shorts a futures contract on the stock
Q2) A trader buys a call and sells a put with the same strike price and maturity date.What is the position equivalent to?
A)A long forward
B)A short forward
C)Buying the asset
D)None of the above
Q3) 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
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12
Chapter 11: Properties of Stock Options
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Sample Questions
Q1) A European call and a European put on a stock have the same strike price and time to maturity.At 10:00am on a certain day,the price of the call is $3 and the price of the put is $4.At 10:01am news reaches the market that has no effect on the stock price or interest rates,but increases volatilities.As a result the price of the call changes to $4.50.Which of the following is correct?
A)The put price increases to $6.00
B)The put price decreases to $2.00
C)The put price increases to $5.50
D)It is possible that there is no effect on the put price
Q2) 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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Chapter 12: Trading Strategies Involving Options
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Q1) How can a strip trading strategy 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
Q2) Which of the following describes a covered call?
A)A long call option on a stock plus a long position in the stock
B)A long call option on a stock plus a short put option on the stock
C)A short call option on a stock plus a short position in the stock
D)A short call option on a stock plus a long position in the stock
Q3) How can a strangle trading strategy 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
Q4) Which of the following creates a bear spread?
A)Buy a low strike price call and sell a high strike price call
B)Buy a high strike price call and sell a low strike price call
C)Buy a low strike price call and sell a high strike price put
D)Buy a low strike price put and sell a high strike price call
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Chapter 13: Binomial Trees
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Q1) which of the following is closest to the Cox,Ross,Rubinstein parameter p for a tree with a three-month time step?
A)0.50
B)0.54
C)0.58
D)0.62
Q2) An investor sells call options with a strike price of $32.Which of the following hedges the position?
A)Buy 0.6 shares for each call option sold
B)Buy 0.4 shares for each call option sold
C)short 0.6 shares for each call option sold
D)Short 0.6 shares for each call option sold
Q3) Which of the following are NOT true
A)Risk-neutral valuation and no-arbitrage arguments give the same option prices
B)Risk-neutral valuation involves assuming that the expected return is the risk-free rate and then discounting expected payoffs at the risk-free rate
C)A hedge set up to value an option does not need to be changed
D)All of the above
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Chapter 14: Wiener Processes and Itos Lemma
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Q1) Which of the following is true when the stock price follows geometric Brownian motion
A)The future stock price has a normal distribution
B)The future stock price has a lognormal distribution
C)The future stock price has geometric distribution
D)The future stock price has a truncated normal distribution
Q2) Which of the following is NOT a property of a Wiener process?
A)The change during a short period of time dt has a variance dt
B)The changes in two different short periods of time are independent
C)The mean change in any time period is zero
D)The standard deviation over two consecutive time periods is the sum of the standard deviations over each of the periods
Q3) If a variable x follows the process dx = b dz where dz is a Wiener process,which of the following is the process followed by y = exp(x).
A)dy = by dz
B)dy = 0.5b<sup>2</sup>y dt+by dz
C)dy = (y+0.5b<sup>2</sup>y) dt+by dz
D)dy = 0.5b<sup>2</sup>y dt+b dz
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Chapter 15: The Black-Scholes-Merton Model
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Q1) A stock provides an expected return of 10% per year and has a volatility of 20% per year.What is the expected value of the continuously compounded return in one year?
A)6%
B)8%
C)10%
D)12%
Q2) When the non-dividend paying stock price is $20,the strike price is $20,the risk-free rate is 6%,the volatility is 20% and the time to maturity is 3 months which of the following is the price of a European call option on the stock
A)20N(0.1)-19.7N(0.2)
B)20N(0.2)-19.7N(0.1)
C)19.7N(0.2)-20N(0.1)
D)19.7N(0.1)-20N(0.2)
Q3) What was the original Black-Scholes-Merton model designed to value?
A)A European option on a stock providing no dividends
B)A European or American option on a stock providing no dividends
C)A European option on any stock
D)A European or American option on any stock
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Chapter 16: Employee Stock Options
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Q1) When an employee stock option is exercised,which of the following is usually true?
A)The employee pays the market price for the shares and the company refunds the difference between the market price and the strike price
B)The company or the company's agent buys stock in the market for the employee
C)The company issues more shares and sells them to the employee for the strike price
D)The employee cannot immediately sell the shares
Q2) Which of the following was true about employee stock options between 1996 and 2004?
A)The options never had any affect on a company's financial statements
B)The value of options which were at-the-money when issued had to be expensed on the income statement
C)The value of options which were at-the-money when issued had to be reported in the notes to the financial statements
D)Options which were at-the-money when issued did not affect a company's financial statements
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Chapter 17: 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 stock prices might decline rapidly during the next six months and would like to use put 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 position is required if the portfolio has a beta of 1?
A)Short 200 contracts
B)Long 200 contracts
C)Short 100 contracts
D)Long 100 contracts
Q2) The domestic risk-free rate is 3%.The foreign risk-free rate is 5%.What is the risk-neutral growth rate of the exchange rate?
A)+2%
B)-2%
C)+5%
D)+3%
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Chapter 18: Futures Options
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Q1) What is the value of a European call futures option where the futures price is 50,the strike price is 50,the risk-free rate is 5%,the volatility is 20% and the time to maturity is three months?
A)49.38N(0.05)-49.38N(-0.05)
B)50N(0.05)-50N(-0.05)
C)49.38N(0.1)-49.38N(-0.1)
D)50N(0.1)-49.38N(-0.1)
Q2) Which of the following is NOT true?
A)Black's model can be used to value an American-style option on futures
B)Black's model can be used to value a European-style option on futures
C)Black's model can be used to value a European-style option on spot
D)Black's model is widely used by practitioners
Q3) Consider a European one-year call futures option and a European one-year put futures options when the futures price equals the strike price.Which of the following is true?
A)The call futures option is worth more than the put futures option
B)The put futures option is worth more than the call futures option
C)The call futures option is sometimes worth more and sometimes worth less than the put futures option
D)The call futures option is worth the same as the put futures option
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Chapter 19: The Greek Letters
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Q1) Which of the following is true?
A)The delta of a European put equals minus the delta of a European call
B)The delta of a European put equals the delta of a European call
C)The gamma of a European put equals minus the gamma of a European call
D)The gamma of a European put equals the gamma of a European call
Q2) The risk-free rate is 5% and the dividend yield on an index is 2%.Which of the following is the delta with respect to the index for a one-year futures on the index?
A)0.98
B)1.05
C)1.03
D)1.02
Q3) Vega 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 short time to maturity
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Chapter 20: Volatility Smiles
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Q1) If the volatility implied from an at-the-money put stock option were used to price other put options on the stock,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 is true when the tails of a future foreign currency distribution are compared with those of a lognormal distribution with the same mean and standard deviation?
A)The left tail and right tail are thinner
B)The left tail is thinner and the right tail is fatter
C)The right tail is thinner and the left tail is fatter
D)Both tails are fatter
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22
Chapter 21: Basic Numerical Procedures
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Q1) Which of the following is true?
A)The implicit finite difference method relates prices at one node to three prices at nodes at a later time
B)The implicit finite difference method relates prices at one node to three prices at nodes at an earlier time
C)The implicit finite difference method relates prices at one node to three prices at nodes at the same time
D)None of the above
Q2) What is the recommended way of making volatility a function of time in a Cox,Ross,Rubinstein tree?
A)Make u a function of time
B)Make p a function of time
C)Make u and p a function of time
D)Make the lengths of the time steps unequal
Q3) Which of the following cannot be estimated from a single binomial tree?
A)delta
B)gamma
C)theta
D)vega
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Page 23
Chapter 22: Value at Risk
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Q1) The 10-day VaR is often assumed to be which of the following
A)The 1-day VaR multiplied by 10
B)The 1-day VaR multiplied by the square root of10
C)The 1-day VaR divided by 10
D)The 1-day VaR divided by the square root of 10
Q2) Which of the following is true
A)Expected shortfall is always less than VaR
B)Expected shortfall is always greater than VaR
C)Expected shortfall is sometimes greater than VaR and sometimes less than VaR
D)Expected shortfall is a measure of liquidity risk wheras VaR is a measure of market risk
Q3) The gain from a project is equally likely to have any value between -$0.15 million and +$0.85 million.What is the 99% expected shortfall?
A)$0.145 million
B)$0.14 million
C)$0.13 million
D)$0.10 million
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Chapter 23: Estimating Volatilities and Correlations
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Q1) Which of the following is true when the parameter lambda equals 0.95?
A)The weight given to the most recent observation is 0.95
B)The weight given to the observation one day ago is 95% of the weight given to the observation two days ago
C)The weights given to observations add up to 0.95
D)The weights given to the observation two days ago is 95% of the weight given to the observation one day ago
Q2) Which of the following is true
A)All option implied volatilities tend to move by the same about from one day to the next
B)The implied volatilities of long-dated options tend to move by more than the implied volatilities of short-dated options
C)The implied volatilities of short-dated options tend to move by more than the implied volatilities of long-dated options
D)Sometimes C is true and sometimes D is true
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Chapter 24: Credit Risk
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Q1) Which of the following is true
A)The asset swap spread is a measure of excess of the bond yield over the OIS rate
B)The asset swap spread is a measure of excess of the bond yield over the LIBOR/swap rate
C)An asset swap exchanges the actual return on the asset for LIBOR plus a spread
D)None of the above
Q2) Which of the following is true
A)Netting always leads to a reduction in a company's exposure to a counterparty
B)Netting always leads to a company's exposure to a counterparty either staying the same or going down
C)Netting always increases a company's exposure to a counterparty
D)Netting can increase or reduce the exposure
Q3) Which of the following is true
A)A derivative dealer's CVA is the counterparty's DVA and vice versa
B)Collateral posted by the counterparty reduces CVA
C)Collateral posted by the dealer reduces DVA
D)All of the above
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Chapter 25: Credit Derivatives
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Q1) Which of the following is true of a synthetic CDO?
A)It is created from portfolios of bonds
B)It is created from portfolios of CDSs
C)It references a standard portfolio of bonds
D)None of the above
Q2) Gaussian quadrature is
A)A quadratic spline approximation to a normal distribution
B)A way to approximate an integral of a function of a normally distribute variable as a sum of terms
C)A procedure for speeding up Monte Carlo simulation when credit derivatives are valued
D)An alternative to a look up table to determining values of the cumulative normal distribution
Q3) In a CDS with a notional principal of $100 million the reference entity defaults.What is the payoff to the buyer of protection when the recovery rate is 30%?
A)$100 million
B)$30 million
C)$130 million
D)$70 million
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Chapter 26: Exotic Options
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Q1) Which of the following is the payoff from an average strike put option?
A)The excess of the strike price over the average stock price, if positive
B)The excess of the final stock price over the average stock price, if positive
C)The excess of the average stock price over the strike price, if positive
D)The excess of the average stock price over the final stock price, if positive
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) A volatility swap is
A)An instrument that swaps the change in the value of a market variable for a fixed amount
B)A swap involving an asset whose volatility is greater than a certain level
C)An exchange of the implied volatility of an option at a future time for a fixed volatility
D)An exchange of the realized volatility of an asset for a fixed volatility
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