A synthetic short put position can be created with which of the following sets of transactions.

A synthetic short put position can be created with which of the following sets of transactions.

a. borrow the present value of the strike price, sell stock, sell call
b. lend the present value of the strike price, sell stock, buy call
c. sell call, buy stock, lend the present value of the strike price
d. buy stock, buy call, borrow the present value of the strike price
e. none of the above creates a synthetic long call position







Answer: C

A synthetic long call position can be created with which of the following sets of transactions.

A synthetic long call position can be created with which of the following sets of transactions.

a. borrow the present value of the strike price, sell stock, sell put
b. lend the present value of the strike price, sell stock, buy put
c. sell put, buy stock, lend the present value of the strike price
d. buy stock, buy put, borrow the present value of the strike price
e. none of the above creates a synthetic long call position

Answer: B

Identify the correct statement related to the choice of exercise price for buying a call.

Identify the correct statement related to the choice of exercise price for buying a call.

a. the higher the exercise price the higher the call premium
b. the lower the exercise price the more likely the call option will expire out-of-the-money
c. A higher strike price results in smaller gains on the upside but smaller losses on the downside
d. the higher the exercise price the more dividends contribute to the overall profit
e. none of the above are correct statements related to the choice of exercise price for buying a call

Answer: C

Which of the following statements about a covered call writing strategy is true?

Which of the following statements about a covered call writing strategy is true?

a. the losses are limited
b. return and risk are greater than that of simply holding the stock
c. it is a cheaper form of insurance than a protective put
d. it generally makes a large number of small profits
e. none of the above





Answer: D

Which of the following investors may be obligated to buy stock?

Which of the following investors may be obligated to buy stock?

a. covered call writer
b. call buyer
c. put writer
d. protective put buyer
e. none of the above




Answer: C

The difference in profit from an actual put and a synthetic put is

The difference in profit from an actual put and a synthetic put is

a. X
b. ST - X
c. X - ST
d. ST + X(1 + r)-T
e. none of the above

Answer: E

Which of the following is the breakeven for a protective put?

Which of the following is the breakeven for a protective put?

a. X + S0 - P
b. P + S0
c. X - ST
d. X - S0 - P
e. none of the above





Answer: B

Which of the following strategies has essentially the same profit diagram as a covered call?

Which of the following strategies has essentially the same profit diagram as a covered call?

a. a long put
b. a short put
c. a protective put
d. a long call
e. none of the above






Answer: B

Which of the following strategies has the greatest potential loss?

Which of the following strategies has the greatest potential loss?

a. an uncovered call
b. a long put
c. a covered call
d. a long position in the stock
e. it is impossible to tell





Answer: A

Each of the following is a bullish strategy except

Each of the following is a bullish strategy except

a. a long call
b. a short put
c. a short stock
d. a protective put
e. none of the above





Answer: C

Early exercise imposes a risk to all but one of the following transactions.

Early exercise imposes a risk to all but one of the following transactions.

a. a short call
b. a short put
c. a protective put
d. an uncovered call
e. none of the above

Answer: C

Which of the following is equivalent to a synthetic call?

Which of the following is equivalent to a synthetic call?

a. a long stock and a short put position
b. a long put and a long stock position
c. a long put and a short risk-free bond position
d. a long stock and a short risk-free bond position
e. none of the above





Answer: B

Which of the following transactions does not profit in a strong bull market.

Which of the following transactions does not profit in a strong bull market.

a. a short put
b. a covered call
c. a protective put
d. a synthetic call
e. none of the above





Answer: E

Which of the following statements is true about closing a long call position prior to expiration relative to holding it to expiration?

Which of the following statements is true about closing a long call position prior to expiration relative to holding it to expiration?

a. the profit is greater at all stock prices
b. the profit is greater only at low stock prices
c. the profit is greater only at high stock prices
d. the range of possible profits is greater
e. none of the above are true





Answer: A

Consider two put options differing only by exercise price. The one with the higher exercise price has

Consider two put options differing only by exercise price. The one with the higher exercise price has

a. the lower breakeven and lower profit potential
b. the lower breakeven and greater profit potential
c. the higher breakeven and greater profit potential
d. the higher breakeven and lower profit potential
e. the greater premium and lower profit potential

Answer: D

S0 = 23 X = 20 rc = 0.09 T = 0.5 2 = 0.15 No dividends are expected.

S0 = 23 X = 20
rc = 0.09 T = 0.5
2 = 0.15
No dividends are expected.

What value does the Black-Scholes-Merton model predict for the call? (Due to differences in rounding your calculations may be slightly different. "none of the above" should be selected only if your answer is different by more than 10 cents.)

a. 5.35
b. 1.10
c. 4.73
d. 6.50
e. none of the above

Answer: C

If we now assume that the stock pays a dividend at a known constant rate of 3.5 percent, what stock price should we use in the model? (Due to differences in rounding your calculations may be slightly different. "none of the above" should be selected only if your answer is different by more than 10 cents.)

a. 22.60
b. 19.65
c. 23.00
d. 21.99
e. none of the above


Answer: A 

The relationship between the option price and the exercise price is called

The relationship between the option price and the exercise price is called 

a. the gamma
b. the vega
c. the omega
d. the zeta
e. none of the above




Answer: E

Which of the following statements about the volatility is not true?

Which of the following statements about the volatility is not true? 

a. the implied volatility often differs across options with different exercise prices
b. the implied volatility equals the historical volatility if the option is correctly priced
c. the implied volatility is determined by trial and error
d. the implied volatility is nearly linearly related to the option price
e. none of the above




Answer: B

Which of the following "Greeks" is not a measure of the option's sensitivity to a change in one of its input values?

Which of the following "Greeks" is not a measure of the option's sensitivity to a change in one of its input values? 

a. delta
b. gamma
c. rho
d. theta
e. sigma





Answer: C

Which of the following statements about the delta is not true?

Which of the following statements about the delta is not true? 

a. it ranges from zero to one
b. it converges to zero or one at expiration
c. it is given by N(d1) in the Black-Scholes-Merton model
d. it changes slowly near expiration if the option is at-the-money
e. none of the above



Answer: D

Which of the following characteristics of the Black-Scholes-Merton model is not correct?

Which of the following characteristics of the Black-Scholes-Merton model is not correct?

a. it is a discrete time model
b. it is the limit of the binomial model
c. it is a continuous time model
d. it gives the price of a European option
e. none of the above





Answer: A

The binomial price will theoretically equal the Black-Scholes-Merton price under which of the following conditions?

The binomial price will theoretically equal the Black-Scholes-Merton price under which of the following conditions?

a. when the number of time periods is large
b. when the option is at-the-money
c. when the option is in-the-money
d. when the option is out-of-the-money
e. none of the above





Answer: A

Which of the following variables in the Black-Scholes-Merton option pricing model is the most difficult to obtain?

Which of the following variables in the Black-Scholes-Merton option pricing model is the most difficult to obtain?

a. the volatility
b. the risk-free rate
c. the stock price
d. the time to expiration
e. the exercise price





Answer: A

Which of the following assumptions of the Black-Scholes-Merton model is not correct?

Which of the following assumptions of the Black-Scholes-Merton model is not correct? 

a. the stock volatility is constant
b. the stock return follows a normal distribution
c. there are no transaction costs
d. there are no taxes
e. none of the above




Answer: B

Which of the following statements about the Black-Scholes-Merton model is not true?

Which of the following statements about the Black-Scholes-Merton model is not true?

a. decreasing the volatility lowers the call price
b. the expected stock price plays a role in the model
c. the risk-free rate is continuously compounded
d. the model is consistent with put-call parity
e. none of the above





Answer: B

The pattern of volatility across exercise prices is often called

The pattern of volatility across exercise prices is often called

a. the price-fluctuation graph
b. the volatility smile
c. the term structure of implied volatility
d. the skew
e. none of the above

Answer: B

The relationship between the volatility and the time to expiration is called the

The relationship between the volatility and the time to expiration is called the

a. volatility smile
b. volatility skew
c. term structure of volatility
d. theta
e. none of the above






Answer: C

What is the reason for executing a gamma hedge?

What is the reason for executing a gamma hedge? 

a. the volatility can change
b. the stock price can make a large move
c. the stock price moves are too small for a delta hedge to work
d. there is no true risk-free rate
e. none of the above






Answer: B

Which of the following statements is true about the relationship between the option price and the risk-free rate?

Which of the following statements is true about the relationship between the option price and the risk-free rate? 

a. a call price is nearly linear with respect to the risk-free rate
b. a call price is highly sensitive to the risk-free rate
c. the risk-free rate affects a call but not a put
d. the risk-free rate does not affect a call price
e. none of the above



Answer: A

If the stock price is 44, the exercise price is 40, the put price is 1.54, and the Black-Scholes-Merton price using 0.28 as the volatility is 1.11, the implied volatility will be

If the stock price is 44, the exercise price is 40, the put price is 1.54, and the Black-Scholes-Merton price using 0.28 as the volatility is 1.11, the implied volatility will be

a. higher than 0.28
b. lower than 0.28
c. 0.28
d. lower than the risk-free rate
e. none of the above

Answer: A

Pricing a put with the binomial model is the same procedure as pricing with a call, except that the

Pricing a put with the binomial model is the same procedure as pricing with a call, except that the

a. underlying stock must not pay dividends
b. binomial model cannot account for expiration payoffs
c. value of the underlying must be discounted back to the current time period
d. expiration payoffs reflect the fact that the option is the right to sell the underlying stock
e. none of the above

Answer: D

Which of the following statements about the binomial model is incorrect?

Which of the following statements about the binomial model is incorrect?

a. it converges to the Black-Scholes-Merton model
b. it can accommodate early exercise
c. it allows only two stock prices at expiration
d. it can be extended to a large number of time periods
e. none of the above

Answer: C

In a one-period binomial model with Su = 49.5, Sd = 40.5, p = 0.8, r = 0.06, S = 45 and X = 50, what is a European put worth?

In a one-period binomial model with Su = 49.5, Sd = 40.5, p = 0.8, r = 0.06, S = 45 and X = 50, what is a European put worth?

a. 2.17
b. 0.50
c. 9.50
d. 5.00
e. none of the above






Answer: A

Suppose S = 70, X = 65, r = 0.05, p = 0.6, Cu = 7.17, Cd = 1.22 and there is one period left in an American call's life. What will the option be worth?

Suppose S = 70, X = 65, r = 0.05, p = 0.6, Cu = 7.17, Cd = 1.22 and there is one period left in an American call's life. What will the option be worth?

a. 6.83
b. 0.00
c. 4.56
d. 5.00
e. none of the above





Answer: C

In the binomial model, if an option has no chance of expiring out-of-the-money, the hedge ratio will be

In the binomial model, if an option has no chance of expiring out-of-the-money, the hedge ratio will be

a. 0.5
b. infinite
c. 1
d. 0
e. none of the above





Answer: E

Consider a binomial world in which the current stock price of 80 can either go up by 10 percent or down by 8 percent. The risk-free rate is 4 percent. Assume a one-period world. Answer questions 12 through 15 about a call with an exercise price of 80.

Consider a binomial world in which the current stock price of 80 can either go up by 10 percent or down by 8 percent. The risk-free rate is 4 percent. Assume a one-period world. Answer questions 12 through 15 about a call with an exercise price of 80.

Question: What would be the call's price if the stock goes up?

a. 3.60
b. 8.00
c. 5.71
d. 4.39
e. none of the above


Answer: B

Question: What would be the call's price if the stock goes down?

a. 8.00
b. 3.60
c. 0.00
d. 9.00
e. none of the above


Answer: C

Question: What is the hedge ratio?

a. 0.429
b. 0.714
c. 0.571
d. 0.823
e. none of the above


Answer: E

Question: What is the theoretical value of the call?

a. 8.00
b. 4.39
c. 5.15
d. 5.36
e. none of the above


Answer: C

When the number of time periods in a binomial model is large, what happens to the binomial probability of an up move?

When the number of time periods in a binomial model is large, what happens to the binomial probability of an up move? 

a. it approaches 1.0
b. it approaches zero
c. it fluctuates without pattern
d. it converges to 0.5
e. none of the above

Answer: A

When the number of time periods in a binomial model is large, a European call option value does what?

When the number of time periods in a binomial model is large, a European call option value does what? 

a. fluctuates around its intrinsic value
b. converges to a specific value
c. increases without limit
d. converges to the European lower bound
e. none of the above




Answer: C

In a non-recombining tree, the number of paths that will occur after three periods is

In a non-recombining tree, the number of paths that will occur after three periods is 

a. three
b. four
c. ten
d. eight
e. six

Answer: D

Which of the following are not path-dependent options when the stock pays a constant dividend yield?

Which of the following are not path-dependent options when the stock pays a constant dividend yield? 

a. European calls and European puts
b. European calls and American puts
c. American puts and European puts
d. American puts and European calls
e. none of the above

Answer: E

If the binomial model is extended to multiple periods for a fixed option life, which of the following adjustments must be made?

If the binomial model is extended to multiple periods for a fixed option life, which of the following adjustments must be made? 

a. the up and down factors must be increased
b. the risk-free rate must be increased
c. the up and down factors and the risk-free rate must be decreased
d. the initial stock price must be proportionately reduced
e. none of the above





Answer: C

When puts are priced with the binomial model, which of the following is true?

When puts are priced with the binomial model, which of the following is true? 

a. the puts must be American
b. the puts cannot be properly hedged
c. the puts will violate put-call parity
d. the hedge ratio is one throughout the tree
e. none of the above

Answer: D

The values of u and d are which of the following?

The values of u and d are which of the following?

a. the return on the stock if it goes up and down, respectively
b. the inverse of the ratio of the up and down probabilities, respectively, and the risk-free rate
c. the normal probabilities of up and down movements, respectively
d. one plus the return on the stock if it goes up and down, respectively
e. none of the above




Answer: D

In a two-period binomial world, a mispriced call will lead to an arbitrage profit if

In a two-period binomial world, a mispriced call will lead to an arbitrage profit if 

a. the proper hedge ratio is maintained over the two periods
b. the hedge portfolio is terminated after one period
c. the option goes from over- to underpriced or vice versa
d. the option remains mispriced over both periods
e. none of the above

Answer: A

In a binomial model, if the call price in the market is higher than the call price given by the model, you should

In a binomial model, if the call price in the market is higher than the call price given by the model, you should 

a. sell the call and sell short the stock
b. buy the call and sell short the stock
c. buy the stock and sell the call
d. buy the call and buy the stock
e. none of the above





Answer: C

A portfolio that combines the underlying stock and a short position in an option is called

A portfolio that combines the underlying stock and a short position in an option is called

a. a risk arbitrage portfolio
b. a hedge portfolio
c. a ratio portfolio
d. a two-state portfolio
e. none of the above





Answer: B

The effect of volatility on a call/put's price is

The effect of volatility on a call/put's price is 

a. decreased price due to decreased possible losses
b. nominal volatility will not noticeably effect a call/put's price
c. increased price due to increased possible gains
d. decreased price due to increased possible losses
e. none of the above




Answer: C

A situation in which early exercise of an American put can be justified is

A situation in which early exercise of an American put can be justified is

a. bankruptcy
b. merger
c. if X exceeds S0 by greater than any transaction costs.
d. both a and b
e. both a and b and c

Answer: A

Suppose that you observe a European option on a currency with an exchange rate of S0 and a foreign risk-free rate of . Which of the following inequalities correctly expresses the lower bound of the call?

Suppose that you observe a European option on a currency with an exchange rate of S0 and a foreign risk-free rate of . Which of the following inequalities correctly expresses the lower bound of the call?

a. Ce(S0,T,X) = Max[0,S0(1 + )-T + X(1 + r)-T]
b. Ce(S0,T,X) = Max[0,S0 - X(1 + )-T]
c. Ce(S0,T,X) = Max[0,S0(1 + )-T - X]
d. Ce(S0,T,X) = Max[0,S0(1 + )-T - X(1 + r)-T]
e. none of the above

Answer: D

Which of the following inequalities correctly states the relationship between the difference in the prices of two European calls that differ only by exercise price

Which of the following inequalities correctly states the relationship between the difference in the prices of two European calls that differ only by exercise price

a. (X2¬ - X1)(1 + r)-T = Ce(S0,T,X1) - Ce(S0,T,X2)
b. (X2¬ - X1) = Ce(S0,T,X2) - Ce(S0,T,X1)
c. (X2 - X1)(1 + r)-T = Ce(S0,T,X1) + Ce(S0,T,X2)
d. (X2¬ - X1) = Ce(S0,T,X1) - Ce(S0,T,X2)
e. none of the above




Answer: A

Given a longer-lived American call and a shorter-lived American call with the same terms, the longer-lived call must always be worth

Given a longer-lived American call and a shorter-lived American call with the same terms, the longer-lived call must always be worth 

a. at most the value of the shorter-lived call
b. at least as much as the shorter-lived call
c. exactly the same as the shorter-lived call
d. the shorter-lived call discounted to the length of the longer-lived call
e. none of the above






Answer: B

Which of the following statements about an American call is not true?

Which of the following statements about an American call is not true?

a. Its time value decreases as expiration approaches
b. Its maximum value is the stock price
c. It can be exercised prior to expiration
d. It pays dividends
e. none of the above

Answer: D

The difference between a Treasury bill's face value and its price is called the

The difference between a Treasury bill's face value and its price is called the

a. time value
b. discount
c. coupon rate
d. bid
e. none of the above

Answer: B

Which of the following is the lowest possible value of an American put on a stock with no dividends?

Which of the following is the lowest possible value of an American put on a stock with no dividends?

a. X(1 + r)-T
b. X
c. Max(0, X(1 + r)-T - S0)
d. Max(0, X - S0)
e. none of the above




Answer: D

Which of the following is the lowest possible value of an American call on a stock with no dividends?

Which of the following is the lowest possible value of an American call on a stock with no dividends?

a. Max(0, S0 - X(1 + r)-T)
b. S0
c. Max(0, S0 - X)
d. Max(0, S0 (1 + r)-T - X)
e. none of the above

Answer: A

The time value of an option is also referred to as the

The time value of an option is also referred to as the

a. synthetic value
b. strike value
c. speculative value
d. parity value
e. none of the above

Answer: C

If there are no dividends on a stock, which of the following statements is correct?

If there are no dividends on a stock, which of the following statements is correct?

a. An American call will sell for more than a European call
b. A European call will sell for more than an American call
c. An American call will be immediately exercised
d. An American call and an American put will sell for the same price
e. none of the above

Answer: E

Suppose you use put-call parity to compute a European call price from the European put price, the stock price, and the risk-free rate. You find the market price of the call to be less than the price given by put-call parity. Ignoring transaction costs, what trades should you do?

Suppose you use put-call parity to compute a European call price from the European put price, the stock price, and the risk-free rate. You find the market price of the call to be less than the price given by put-call parity. Ignoring transaction costs, what trades should you do?

a. buy the call and the risk-free bonds and sell the put and the stock
b. buy the stock and the risk-free bonds and sell the put and the call
c. buy the put and the stock and sell the risk-free bonds and the call
d. buy the put and the call and sell the risk-free bonds and the stock

Answer: A

On March 2, a Treasury bill expiring on April 20 had a bid discount of 5.80, and an ask discount of 5.86. What is the best estimate of the risk-free rate as given in the text?

On March 2, a Treasury bill expiring on April 20 had a bid discount of 5.80, and an ask discount of 5.86. What is the best estimate of the risk-free rate as given in the text?

a. 5.86 %
b. 5.83 %
c. 6.11 %
d. 6.14 %
e. none of the above







Answer: C

Another expression for intrinsic value is

Another expression for intrinsic value is

a. parity
b. parity value
c. exercise value
d. all of the above
e. none of the above

Answer: D

What is the lowest possible value of a European put?

What is the lowest possible value of a European put?

a. Max(0, X - S0)
b. X(1 + r)-T
c. Max[0, S0 - X(1 + r)-T]
d. Max[0, X(1 + r)-T - S0)]
e. none of the above

Answer: D

Consider a portfolio consisting of a long call with an exercise price of X, a short position in a non-dividend paying stock at an initial price of S0, and the purchase of riskless bonds with a face value of X and maturing when the call expires. What should such a portfolio be worth?

Consider a portfolio consisting of a long call with an exercise price of X, a short position in a non-dividend paying stock at an initial price of S0, and the purchase of riskless bonds with a face value of X and maturing when the call expires. What should such a portfolio be worth?

a. C + P - X(1 + r)-T
b. C - S0
c. P - X
d. P + S0 - X(1 + r)-T
e. none of the above

Answer: E