69) You would like to hold a protective put position on the stock of Avalon Corporation to lock
in a guaranteed minimum value of $50 at year-end. Avalon currently sells for $50. Over the next
year, the stock price will increase by 10% or decrease by 10%. The T-bill rate is 5%.
Unfortunately, no put options are traded on Avalon Co.
What portfolio position in stock and T-bills will ensure you a payoff equal to the payoff that
would be provided by a protective put with X = $50?
A) ½ share of stock and $25 in bills
B) 1 share of stock and $50 in bills
C) ½ share of stock and $26.19 in bills
D) 1 share of stock and $25 in bills
70) You calculate the Black-Scholes value of a call option as $3.50 for a stock that does not pay
dividends, but the actual call price is $3.75. The most likely explanation for the discrepancy is
that either the option is ________ or the volatility you input into the model is too ________.
A) overvalued and should be written; low
B) undervalued and should be written; low
C) overvalued and should be purchased; high
D) undervalued and should be purchased; high
71) What combination of variables is likely to lead to the lowest time value?
A) short time to expiration and low volatility
B) long time to expiration and high volatility
C) short time to expiration and high volatility
D) long time to expiration and low volatility
72) The time value of a call option is likely to decline most rapidly ________ days before
expiration?
A) 10
B) 30
C) 60
D) 90
73) The fact that American put values may not equal the price implied by put-call parity is
attributable to the possibility of what event?
A) changes in the dividend
B) early exercise
C) interest rate declines
D) interest rate rises
74) Calculate the price of a call option using the Black Scholes model and the following data:
stock price = $47.30, exercise price = $50, time to expiration = 85 days, risk-free rate = 3%,
standard deviation = 35%.
A) $1.11
B) $2.22
C) $3.33
D) $4.44
75) Calculate the price of a European call option using the Black Scholes model and the
following data: stock price = $56.80, exercise price = $55, time to expiration = 15 days, risk-free
rate = 2.5%, standard deviation = 22%, dividend yield = 8%.
A) $1.49
B) $1.79
C) $2.19
D) $2.29
76) The intrinsic value of an out-of-the-money call option ________.
A) is negative
B) is positive
C) is zero
D) cannot be determined
77) A call option has an exercise price of $30 and a stock price of $34. If the call option is
trading for $5.25, what is the intrinsic value of the option?
A) $0
B) $1.25
C) $4
D) $5.25
78) A call option has an exercise price of $35 and a stock price of $36.50. If the call option is
trading at $2.25, what is the time value embedded in the option?
A) $0
B) $0.75
C) $1.50
D) $2.25
79) What aspect of the time value of money does the factor of e represent in the Black-Scholes
option value formula?
A) annual compounding
B) compounding at the expiration time frame
C) continuous compounding
D) daily compounding
80) Suppose you purchase a call and write a put on the same stock with the same exercise price
and expiration. If prices are at equilibrium, the value of this portfolio is ________.
A) S0 − Xe−rt
B) S0 − X
C) S0 + Xe−rt
D) S0 + X
81) A stock priced at $65 has a standard deviation of 30%. Three-month calls and puts with an
exercise price of $60 are available. The calls have a premium of $7.27, and the puts cost $1.10.
The risk-free rate is 5%. Since the theoretical value of the put is $1.525, you believe the puts are
undervalued.
If you want to construct a riskless arbitrage to exploit the mispriced puts, you should ________.
A) buy the call and sell the put
B) write the call and buy the put
C) write the call and buy the put and buy the stock and borrow the present value of the exercise
price
D) buy the call and buy the put and short the stock and lend the present value of the exercise
price
82) A stock priced at $65 has a standard deviation of 30%. Three-month calls and puts with an
exercise price of $60 are available. The calls have a premium of $7.27, and the puts cost $1.10.
The risk-free rate is 5%. Since the theoretical value of the put is $1.525, you believe the puts are
undervalued.
If you construct a riskless arbitrage to exploit the mispriced puts, your arbitrage profit will be
________.
A) $5.75
B) $6.17
C) $0.96
D) $0.42
83) The option smirk in the Black-Scholes option model indicates that ________.
A) implied volatility changes unpredictably as the exercise price rises
B) stock prices may fall by a larger amount than the model assumes
C) stock prices evolve continuously in today’s actively traded markets
D) stocks with lower exercise prices are more likely to pay dividends
84) A put option has a strike price of $35 and a stock price of $38. If the put option is trading at
$1.25, what is the time value embedded in the option?
A) $0
B) $0.75
C) $1.25
D) $3
85) Hedge ratios for long puts are always ________.
A) between −1 and 0
B) between 0 and 1
C) 1
D) greater than 1
86) Which combination of stock, exercise, and option prices are most likely associated with an
American call option?
A) stock = $60, exercise = $65, option = $5
B) stock = $65, exercise = $60, option = $5
C) stock = $65, exercise = $60, option = $7
D) stock = $60, exercise = $65, option = $7
87) A stock with a stock and exercise price of $20 can either increase to $26 or decrease to $18
over the course of one year. In a one-period binomial option model, given an interest rate of 5%
and equal probabilities, what is the likely option price? (Use annual compounding.)
A) $2.36
B) $2.50
C) $2.88
D) $3.00
88) Given a stock price of $18, an exercise price of $20, and an interest rate of 7%, what are the
intrinsic values which will occur for a one-period binomial option model if the stock price goes
up to $23 or down to $16?
A) $3 and $0
B) $3 and −$4
C) $4 and $3
D) $4 and $2
89) In order for a binomial option price to approach the Black Scholes price, ________.
A) the number of subintervals must increase substantially
B) the volatility must be low
C) the probability of each subinterval needs to be similar to the stock’s standard deviation
D) the interest rate needs to increase
90) The current stock price of KMW is $27, the risk-free rate of return is 4%, and the standard
deviation is 30%. What is the price of a 63-day call option with an exercise price of $25?
A) $2.50
B) $2.65
C) $2.89
D) $3.12