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12. A stock provides an expected return of 10% per year and has a volatility of 20% per year. What is the continuously compounded expected return in one year? A. 6% B. 8% C. 10% D. 12%

: B

19. Which of the following is NOT a letter in the Greek alphabet? A. delta B. rho C. vega D. gamma

: C

5. What does rho measure? A. The rate of change of delta with the asset price B. The rate of change of the portfolio value with the passage of time C. The sensitivity of a portfolio value to interest rate changes D. None of the above

: C

19. A stock price is 20, 22, 19, 21, 24, and 24 on six successive Fridays. Which of the following is closest to the volatility per annum estimated from this data? A. 50% B. 60% C. 70% D. 80%

: D

2. The original Black-Scholes and Merton papers on stock option pricing were published in which year? A. 1983 B. 1984 C. 1974 D. 1973

: D

0 8.Which of the following is an example of an option class? A.All calls on a certain stock B.All calls with a particular strike price on a certain stock C.All calls with a particular time to maturity on a certain stock D.All calls with a particular time to maturity and strike price on a certain stock

A An option class is all calls on a certain stock or all puts on a certain stock. 150

18. What is the size of one option contract on the S&P 500? A. 250 times the index B. 100 times the index C. 50 times the index D. 25 times the index

B

19. 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%

B

0 11.Which of the following describes a situation where an American put option on a stock becomes more likely to be exercised early? A.Expected dividends increase B.Interest rates decrease C.The stock price volatility decreases D.All of the above

C As the volatility of the option decreases the time value declines and the option becomes more likely to be exercised early. In the case of A and B, time value increases and the option is less likely to be exercised early. 172

0 1.Which of the following describes LEAPS? A.Options which are partly American and partly European B.Options where the strike price changes through time C.Exchange-traded stock options with longer lives than regular exchange-traded stock options D.Options on the average stock price during a period of time

C LEAPS are long-term equity anticipation securities. They are exchange-traded options with relatively long maturities. 149

17. Which of the following is true when a European currency option is valued using forward exchange rates? A. It is not necessary to know the domestic interest rate or the spot exchange rate B. It is not necessary to know either the foreign or domestic interest rate C. It is necessary to know the difference between the foreign and domestic interest rates but not the rates themselves D. It is not necessary to know the foreign interest rate or the spot exchange rate

D

0 2.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

D Strike price increases cause the values of puts to increase and the values of calls to decline. 163

12. Which of the following is NOT true about a range forward contract? A. It ensures that the exchange rate for a future transaction will lie between two values B. It can be structured so that it costs nothing to set up C. It is constructed from two options and a forward contract D. It can be used to hedge either a future inflow or a future outflow of a foreign currency

C

16. 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

: A

4. 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

: B

15. Which of the following is a way of extending the Black-Scholes-Merton formula to value a European call option on a stock paying a single dividend? A. Reduce the maturity of the option so that it equals the time of the dividend B. Subtract the dividend from the stock price C. Add the dividend to the stock price D. Subtract the present value of the dividend from the stock price

: D

0 16.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

A From adding up the two payoffs we see that A is true: max(ST−K,0)−max(K−ST,0)= ST−K 158

14. A binomial tree with one-month time steps is used to value an index option. The interest rate is 3% per annum and the dividend yield is 1% per annum. The volatility of the index is 16%. What is the probability of an up movement? A. 0.4704 B. 0.5065 C. 0.5592 D. 0.5833

B

15. A European at-the-money call option on a currency has four years until maturity. The exchange rate volatility is 10%, the domestic risk-free rate is 2% and the foreign risk-free rate is 5%. The current exchange rate is 1.2000. What is the value of the option? A. 0.98N(0.25)-1.11(0.05) B. 0.98N(-0.3)-1.11N(-0.5) C. 0.98N(-0.5)-1.11N(-0.7) D. 0.98N(0.10)-1.11N(0.06)

C

6. 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

: D

11. 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

: A

7. What is the number of trading days in a year usually assumed for equities? A. 365 B. 252 C. 262 D. 272

: B

Which of the following describes a call option? A.The right to buy an asset for a certain price B.The obligation to buy an asset for a certain price C.The right to sell an asset for a certain price D.The obligation to sell an asset for a certain price

A A call option is the right, but not the obligation to buy. 142

0 9.Which of the following is NOT true? (Present values are calculated from the end of the life of the option to the beginning.) A.An American put option is always worth less than the present value of the strike price B.A European put option is always worth less than the present value of the strike price C.A European call option is always worth less than the stock price D.An American call option is always worth less than the stock price

A If it is optimal to exercise an American option today and the stock price is very low the option will be worth more than the present value of the strike price 170

3. What should the continuous dividend yield be replaced by when options on an exchange rate are valued using the formula for an option of a stock paying a continuous dividend yield? A. the domestic risk-free rate B. the foreign risk-free rate C. the foreign risk-free rate minus the domestic risk-free rate D. none of the above

B

0 3.An investor has exchange-traded put options to sell 100 shares for $20. There is a 2 for 1 stock split. Which of the following is the position of the investor after the stock split? A.Put options to sell 100 shares for $20 B.Put options to sell 100 shares for $10 C.Put options to sell 200 shares for $10 D.Put options to sell 200 shares for $20

C When there is a stock split the number of shares increases and the strike price decreases. In this case, because it is a 2 for 1 stock split, the number of shares doubles and the strike price halves. 144

12. 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

: A

14. Which of the following is NOT true? A. Risk-neutral valuation assumes that investors are risk neutral B. Options can be valued based on the assumption that investors are risk neutral C. In risk-neutral valuation the expected return on all investment assets is set equal to the risk-free rate D. In risk-neutral valuation the risk-free rate is used to discount expected cash flows

: A

15. The gamma of a delta-neutral portfolio is 500. What is the impact of a jump of $3 in the price of the underlying asset? A. A gain of $2,250 B. A loss of $2,250 C. A gain of $750 D. A loss of $750

: A

18. When the non-dividend paying stock price is $20, the strike price is $20, the risk-free rate is 5%, the volatility is 20% and the time to maturity is 3 months which of the following is the price of a European put option on the stock A. 19.7N(-0.1)-20N(-0.2) B. 20N(-0.1)-20N(-0.2) C. 19.7N(-0.2)-20N(-0.1) D. 20N(-0.2)-20N(-0.1)

: A

3. What does gamma measure? A. The rate of change of delta with the asset price B. The rate of change of the portfolio value with the passage of time C. The sensitivity of a portfolio value to interest rate changes D. None of the above

: A

3. Which of the following is a definition of volatility A. The standard deviation of the return, measured with continuous compounding, in one year B. The variance of the return, measured with continuous compounding, in one year C. The standard deviation of the stock price in one year D. The variance of the stock price in one year

: A

7. A portfolio of derivatives on a stock has a delta of 2400 and a gamma of -10. An option on the stock with a delta of 0.5 and a gamma of 0.04 can be traded. What position in the option is necessary to make the portfolio gamma neutral? A. Long position in 250 options B. Short position in 250 options C. Long position in 20 options D. Short position in 20 options

: A

1. A call option on a stock has a delta of 0.3. A trader has sold 1,000 options. What position should the trader take to hedge the position? A. Sell 300 shares B. Buy 300 shares C. Sell 700 shares D. Buy 700 shares

: B

1. Which of the following is assumed by the Black-Scholes-Merton model? A. The return from the stock in a short period of time is lognormal B. The stock price at a future time is lognormal C. The stock price at a future time is normal D. None of the above

: B

10. Which of the following could NOT be a delta-neutral portfolio? A. A long position in call options plus a short position in the underlying stock B. A short position in call options plus a short position in the underlying stock C. A long position in put options and a long position in the underlying stock D. A long position in a put option and a long position in a call option

: B

17. 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)

: B

18. A call option on a non-dividend-paying stock has a strike price of $30 and a time to maturity of six months. The risk-free rate is 4% and the volatility is 25%. The stock price is $28. What is the delta of the option? A. N(-0.1342) B. N(-0.1888) C. N(-0.2034) D. N(-0.2241)

: B

2. What does theta measure? A. The rate of change of delta with the asset price B. The rate of change of the portfolio value with the passage of time C. The sensitivity of a portfolio value to interest rate changes D. None of the above

: B

5. What does N(x) denote? A. The area under a normal distribution from zero to x B. The area under a normal distribution up to x C. The area under a normal distribution beyond x D. The area under the normal distribution between -x and x

: B

9. Maintaining a delta-neutral portfolio is an example of which of the following A. Stop-loss strategy B. Dynamic hedging C. Hedge and forget strategy D. Static hedging

: B

10. Which of the following is measured by the VIX index A. Implied volatilities for stock options trading on the CBOE B. Historical volatilities for stock options trading on CBOE C. Implied volatilities for options trading on the S&P 500 index D. Historical volatilities for options trading on the S&P 500 index

: C

11. Which of the following is NOT true about gamma? A. A highly positive or highly negative value of gamma indicates that a portfolio needs frequent rebalancing to stay delta neutral B. The magnitude of gamma is a measure of the curvature of the portfolio value as a function of the underlying asset price C. A big positive value for gamma indicates that a big movement in the asset price in either direction will lead to a loss D. A long position in either a call or a put has a positive gamma

: C

13. Which of the following is true for a call option on a non-dividend-paying stock? A. If the option is at the money (stock price equals strike price) it must have a delta of 0.5 B. If the strike price equals the forward price of the stock, it must have a delta of 0.5 C. If the option has a delta of 0.5, it must be out of the money D. If the option has a delta of 0.5, it must be in of the money

: C

14. 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 of a one-year futures on the index? A. 0.98 B. 1.05 C. 1.03 D. 1.02

: C

17. The delta of a call option on a non-dividend-paying stock is 0.4. What is the delta of the corresponding put option? A. -0.4 B. 0.4 C. -0.6 D. 0.6

: C

20. 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

: C

8. The risk-free rate is 5% and the expected return on a non-dividend-paying stock is 12%. Which of the following is a way of valuing a derivative? A. Assume that the expected growth rate for the stock price is 17% and discount the expected payoff at 12% B. Assuming that the expected growth rate for the stock price is 5% and discounting the expected payoff at 12% C. Assuming that the expected growth rate for the stock price is 5% and discounting the expected payoff at 5% D. Assuming that the expected growth rate for the stock price is 12% and discounting the expected payoff at 5%

: C

13. An investor has earned 2%, 12% and -10% on equity investments in successive years (annually compounded). This is equivalent to earning which of the following annually compounded rates for the three year period. A. 1.33% B. 1.23% C. 1.13% D. 0.93%

: D

16. When the Black-Scholes-Merton and binomial tree models are used to value an option on a non-dividend-paying stock, which of the following is true? A. The binomial tree price converges to a price slightly above the Black-Scholes-Merton price as the number of time steps is increased B. The binomial tree price converges to a price slightly below the Black-Scholes-Merton price as the number of time steps is increased C. Either A or B can be true D. The binomial tree price converges to the Black-Scholes-Merton price as the number of time steps is increased

: D

20. When the interest rate is zero which of the following is true for a delta-neutral portfolio with a positive gamma? A. As gamma increases theta becomes more positive B. As gamma decreases theta declines C. Theta is zero D. As gamma increases theta becomes more negative

: D

4. What does vega measure? A. The rate of change of delta with the asset price B. The rate of change of the portfolio value with the passage of time C. The sensitivity of a portfolio value to interest rate changes D. None of the above

: D

6. 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

: D

8. 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

: D

9. When there are two dividends on a stock, Black's approximation sets the value of an American call option equal to which of the following A. The value of a European option maturing just before the first dividend B. The value of a European option maturing just before the second (final) dividend C. The greater of the values in A and B D. The greater of the value in B and the value assuming no early exercise

: D

10. For a European call option on a currency, the exchange rate is 1.0000, the strike price is 0.9100, the time to maturity is one year, the domestic risk-free rate is 5% per annum, and the foreign risk-free rate is 3% per annum. How low can the option price be without there being an arbitrage opportunity? A. 0.1048 B. 0.0900 C. 0.1344 D. 0.1211

A

13. 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

A

16. A European at-the-money call option on a currency has four years until maturity. The exchange rate volatility is 10%, the domestic risk-free rate is 2% and the foreign risk-free rate is 5%. The current exchange rate is 1.2000. What is the value of the option? A. 1.11N(0.7)-0.98N(0.5) B. 1.11N(-0.7)-0.98N(-0.5) C. 1.11N(0.7)-0.98N(0.4) D. 1.11N(-0.06)-0.98N(-0.10)

A

5. 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 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

A

0 5.An investor has exchange-traded put options to sell 100 shares for $20. There is a $1 cash dividend. Which of the following is then the position of the investor? A.The investor has put options to sell 100 shares for $20 B.The investor has put options to sell 100 shares for $19 C.The investor has put options to sell 105 shares for $19 D.The investor has put options to sell 105 shares for $19.05

A Cash dividends unless they are unusually large have no effect on the terms of an option. 146

0 13.When a six-month option is purchased A.The price must be paid in full B.Up to 25% of the option price can be borrowed using a margin account C.Up to 50% of the option price can be borrowed using a margin account D.Up to 75% of the option price can be borrowed using a margin account

A Only options lasting more than 9 months can be bought on margin. 155

0 Which of the following creates a bull 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

A A bull spread is created by buying a low strike call and selling a high strike call. Alternatively, it can be created by buying a low strike put and selling a high strike put.

0 19.Which of the following is true for American options? A.Put-call parity provides an upper and lower bound for the difference between call and put prices B.Put call parity provides an upper bound but no lower bound for the difference between call and put prices C.Put call parity provides an lower bound but no upper bound for the difference between call and put prices D.There are no put-call parity results

A Put call parity provides both an upper and lower bound for the difference between call and put prices. See equation (11.11). 180

0 10.Which of the following best describes the intrinsic value of an option? A.The value it would have if the owner had to exercise it immediately or not at all 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

A The intrinsic value of an option is the value it would have if it were about the expire which is the same as the value in A. 171

0 10.Which of the following must post margin? A.The seller of an option B.The buyer of an option C.The seller and the buyer of an option D.Neither the seller nor the buyer of an option

A The seller of the option must post margin as a guarantee that the payoff on the option (if there is one) will be made. The buyer of the option usually pays for the option upfront and so no margin is required. 152

0 3.When volatility 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

A Volatility increases the likelihood of a high payoff from either a call or a put option. The payoff can never be negative. It follows that as volatility increases the value of all options increase. 164

1. Which of the following describes what a company should do to create a range forward contract in order to hedge foreign currency that will be received? A. Buy a put and sell a call on the currency with the strike price of the put higher than that of the call B. Buy a put and sell a call on the currency with the strike price of the put lower than that of the call C. Buy a call and sell a put on the currency with the strike price of the put higher than that of the call D. Buy a call and sell a put on the currency with the strike price of the put lower than that of the call

B

0 7.Which of the following describes a difference between a warrant and an exchange-traded stock option? A.In a warrant issue, someone has guaranteed the performance of the option seller in the event that the option is exercised B.The number of warrants is fixed whereas the number of exchange-traded options in existence depends on trading C.Exchange-traded stock options have a strike price D.Warrants cannot be traded after they have been purchased

B A warrant is a fixed number of options issued by a company. They often trade on an exchange after they have been issued. 148

0 12.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

B An American call option should never be exercised early when the underlying stock does not pay dividends. There are two reasons. First, it is best to delay paying the strike price. Second the insurance provided by the option (that the stock price will fall below the strike price) is lost. 173

0 20.Which of the following can be used to create a long position in a European put option on a stock? A.Buy a call option on the stock and buy the stock B.Buy a call on the stock and short the stock C.Sell a call option on the stock and buy the stock D.Sell a call option on the stock and sell the stock

B As payoff diagrams show a call on a stock combined with a short position in the stock gives a payoff similar to a put option. Alternatively we can use put-call parity, which shows that a call minus the stock equals the put minus the present value of the strike price. 181

0 14.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

B Margin accounts for options must be brought up to the initial/maintenance margin level every day. 156

0 12.Which of the following is NOT traded by the CBOE? A.Weeklys B.Monthlys C.Binary options D.DOOM options

B Monthlys are not a CBOE product. The others are. 154

0 19.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

B Profits on the asset have to be recognized in A, C, and D. The holder of the asset cannot defer recognition of profits with the trades indicated. In the case of B the asset is not considered constructively sold. Buying a deep-in-the-money put option is a way of almost certainly locking in a profit on an asset without triggering an immediate tax liability. 161

0 14.Which of the following is true when dividends are expected? A.Put-call parity does not hold B.The basic put-call parity formula can be adjusted by subtracting the present value of expected dividends from the stock price C.The basic put-call parity formula can be adjusted by adding the present value of expected dividends to the stock price D.The basic put-call parity formula can be adjusted by subtracting the dividend yield from the interest rate

B Put call parity still holds for European options providing the present value of the dividends is subtracted from the stock price. 175

0 7.The price of a stock, which pays no dividends, is $30 and the strike price of a one year European call option on the stock is $25. The risk-free rate is 4% (continuously compounded). Which of the following is a lower bound for the option such that there are arbitrage opportunities if the price is below the lower bound and no arbitrage opportunities if it is above the lower bound? A.$5.00 B.$5.98 C.$4.98 D.$3.98

B The lower bound in S0 − Ke-rT. In this case it is 30 - 25e-0.04×1 = $5.98. 168

4. Suppose that the domestic risk free rate is r and dividend yield on an index is q. How should the put-call parity formula for options on a non-dividend-paying stock be changed to provide a put-call parity formula for options on a stock index? Assume the options last T years. A. The stock price is replaced by the value of the index multiplied by exp(qT) B. The stock price is replaced by the value of the index multiplied by exp(rT) C. The stock price is replaced by the value of the index multiplied by exp(-qT) D. The stock price is replaced by the value of the index multiplied by exp(-rT)

C

6. 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 1? A. 425 B. 450 C. 475 D. 500

C

7. 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 position is required if the portfolio has a beta of 0.5? A. Short 200 contracts B. Long 200 contracts C. Short 100 contracts D. Long 100 contracts

C

0 11.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

C A long position is a position where an option has been purchased. It can be contrasted with a short position which is a position where an option has been sold. 153

0 5.When interest rates increase 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

C Calls increase and puts decrease in value. As explained in the text an increase in interest rates causes the growth rate of the stock price to increase and the discount rate to increase. An increase in interest rates therefore reduces the value of puts because puts are hurt by both a discount rate increase and a growth rate increase. For calls it turns out that the growth rate increase is more important than the discount rate increase so that their values increase when interest rates increase. (Note that we are assuming all else equal and so the asset price does not change.) 166

0 16.The price of a European call option on a stock with a strike price of $50 is $6. The stock price is $51, the continuously compounded risk-free rate (all maturities) is 6% and the time to maturity is one year. A dividend of $1 is expected in six months. What is the price of a one-year European put option on the stock with a strike price of $50? A.$8.97 B.$6.97 C.$3.06 D.$1.12

C Put-call parity is c+Ke-rT=p+S0. In this case K=50, S0=51, r=0.06, T=1, and c=6. The present value of the dividend is 1×e−0.06×0.5 = 0.97. It follows that p=6+50e-0.06×1−(51-0.97) = 3.06 177

0 1.When the stock 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

C Stock price increases cause the values of calls to increase and the values of puts to decline. 162

0 15.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

C The option payoff is 70−69 = $1. The amount received for the option is $4. The gain is $3 per option. In total 5×100 = 500 options are sold. The total gain is therefore $3 × 500 = $1,500. 157

0 17. 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

C The price of the call has increased by $1.50. From put-call parity the price of the put must increase by the same amount. Hence the put price will become 4.00 +1.50 = $5.50. 178

11. Index put options are used to provide protection against the value of the portfolio falling below a certain level. Which of the following is true as the beta of the portfolio increases? A. The cost of hedging increases B. The options require a lower strike price C. The number of options required increases D. All of the above

D

2. Which of the following describes what a company should do to create a range forward contract in order to hedge foreign currency that will be paid? A. Buy a put and sell a call on the currency with the strike price of the put higher than that of the call B. Buy a put and sell a call on the currency with the strike price of the put lower than that of the call C. Buy a call and sell a put on the currency with the strike price of the put higher than that of the call D. Buy a call and sell a put on the currency with the strike price of the put lower than that of the call

D

20. What is the same as 100 call options to buy one unit of currency A with currency B at a strike price of 1.25? A. 100 call options to buy one unit of currency B with currency A at a strike price of 0.8 B. 125 call options to buy one unit of currency B with currency A at a strike price of 0.8 C. 100 put options to sell one unit of currency B for currency A at a strike price of 0.8 D. 125 put options to sell one unit of currency B for currency A at a strike price of 0.8

D

8. 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

D

9. For a European put option on an index, the index level is 1,000, the strike price is 1050, the time to maturity is six months, the risk-free rate is 4% per annum, and the dividend yield on the index is 2% per annum. How low can the option price be without there being an arbitrage opportunity? A. $50.00 B. $43.11 C. $29.21 D. $39.16

D

0 6.Which of the following describes a short position in an option? A.A position in an option lasting less than one month B.A position in an option lasting less than three months C.A position in an option lasting less than six months D.A position where an option has been sold

D A short position is a position where the option has been sold (the opposite to a long position). 147

0 9.Which of the following is an example of an option series? A.All calls on a certain stock B.All calls with a particular strike price on a certain stock C.All calls with a particular time to maturity on a certain stock D.All calls with a particular time to maturity and strike price on a certain stock

D All options on a certain stock of a certain type (calls or put) with a certain strike price and time to maturity are referred to as an option series 151

2 4.When dividends increase 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

D Dividends during the life of an option reduce the final stock price. As a result dividend increases cause puts to increase in value and calls to decrease in value. 165

0 18.Consider a put option and a call option with the same strike price and time to maturity. Which of the following is true? A.It is possible for both options to be in the money B.It is possible for both options to be out of the money C.One of the options must be in the money D.One of the options must be either in the money or at the money

D If the stock price is greater than the strike price the call is in the money and the put is out of the money. If the stock price is less than the strike price the call is out of the money and the put is in the money. If the stock price is equal to the strike price both options are at the money. 160

0 18.Interest rates are zero. A European call with a strike price of $50 and a maturity of one year is worth $6. A European put with a strike price of $50 and a maturity of one year is worth $7. The current stock price is $49. Which of the following is true? A.The call price is high relative to the put price B.The put price is high relative to the call price C.Both the call and put must be mispriced D.None of the above

D In this case because interest rates are zero c+K=p+S0. The left side of this equation is 50+6=56. The right side is 49+7=56. There is no mispricing. 179

0 2.Which of the following is true? A.A long call is the same as a short put B.A short call is the same as a long put C.A call on a stock plus a stock the same as a put D.None of the above

D None of the statements are true. Long calls, short calls, long puts, and short puts all have different payoffs as indicated by Figure 10.5. A put on a stock plus the stock provides a payoff that is similar to a call, as explained in Chapters 11 and 12. But a call on a stock plus a stock does not provide a similar payoff to a put. 143

0 15.The price of a European call option on a non-dividend-paying stock with a strike price of $50 is $6. The stock price is $51, the continuously compounded risk-free rate (all maturities) is 6% and the time to maturity is one year. What is the price of a one-year European put option on the stock with a strike price of $50? A.$9.91 B.$7.00 C.$6.00 D.$2.09

D Put-call parity is c+Ke-rT=p+S0. In this case K=50, S0=51, r=0.06, T=1, and c=6. It follows that p=6+50e-0.06×1−51 = 2.09. 176

0 8.A stock price (which pays no dividends) is $50 and the strike price of a two year European put option is $54. The risk-free rate is 3% (continuously compounded). Which of the following is a lower bound for the option such that there are arbitrage opportunities if the price is below the lower bound and no arbitrage opportunities if it is above the lower bound? A.$4.00 B.$3.86 C.$2.86 D.$0.86

D The lower bound in Ke-rT −S0 In this case it is 54e−0.03×2 - 50= $0.86. 169

0 13.Which of the following is the put-call parity result for a non-dividend-paying stock? A.The European put price plus the European call price must equal the stock price plus the present value of the strike price B.The European put price plus the present value of the strike price must equal the European call price plus the stock price C.The European put price plus the stock price must equal the European call price plus the strike price D.The European put price plus the stock price must equal the European call price plus the present value of the strike price

D The put-call parity result is c+Ke-rT=p+S0. 174

0 4.An investor has exchange-traded put options to sell 100 shares for $20. There is 25% stock dividend. Which of the following is the position of the investor after the stock dividend? A.Put options to sell 100 shares for $20 B.Put options to sell 75 shares for $25 C.Put options to sell 125 shares for $15 D.Put options to sell 125 shares for $16

D The stock dividend is equivalent to a 5 for 4 stock split. The number of shares goes up by 25% and the strike price is reduced to 4/5 of its previous value. 145

0 6.When the time to maturity increases with all else remaining the same, which of the following is true? A.European options always increase in value B.The value of European options either stays the same or increases C.There is no effect on European option values D.European options are liable to increase or decrease in value

D When the time to maturity increases from X to Y, European options usually increase in value. But they can decrease in value if a big dividend expected between X and Y. 167

0 17.The price of a stock is $64. A trader buys 1 put option contract on the stock with a strike price of $60 when the option price is $10. When does the trader make a profit? A.When the stock price is below $60 B.When the stock price is below $64 C.When the stock price is below $54 D.When the stock price is below $50

D The payoff must be more than the $10 paid for the option. The stock price must therefore be below $50. 159