Multiple Choice Questions
1. If the Black-Scholes formula is solved to find the standard deviation consistent with the
current market call premium, that standard deviation would be called the _______.
A. variability
B. volatility
C. implied volatility
D. deviance
Answer: C. implied volatility
2. The __________ is the stock price minus exercise price, or the profit that could be attained
by immediate exercise of an in-the-money call option.
A. intrinsic value
B. time value
C. stated value
D. discounted value
Answer: A. intrinsic value
3. The _________ is the difference between the actual call price and the intrinsic value.
A. stated value
B. strike value
C. time value
D. binomial value
Answer: C. time value
4. A call option with several months until expiration has a strike price of $55 when the stock
price is $50. The option has _____ intrinsic value and _____ time value.
A. negative; positive
B. positive; negative
C. zero; zero
D. zero; positive
Answer: D. zero; positive
5. All else equal, call option values are _____ if the _____ is lower.
A. higher; stock price
B. higher; exercise price
C. lower; dividend payout
D. lower; stock volatility
Answer: B. higher; exercise price
6. A __________ is an option valuation model based on the assumption that stock prices can
move to only two values over any short time period.
A. nominal model
B. binomial model
C. time model
D. Black-Scholes model
Answer: B. binomial model
7. The Black-Scholes option-pricing formula was developed for __________.
A. American options
B. European options
C. Tokyo options
D. out-of-the-money options
Answer: B. European options
8. A put option with several months until expiration has a strike price of $55 when the stock
price is $50. The option has _____ intrinsic value and _____ time value.
A. negative; positive
B. positive; positive
C. zero; zero
D. zero; positive
Answer: B. positive; positive
9. The hedge ratio is often called the option's _______.
A. delta
B. gamma
C. theta
D. beta
Answer: A. delta
10. A 45 call option on a stock priced at $50 is priced at $6.50. This call has an intrinsic value
of ______ and a time value of _____.
A. $6.50; $0
B. $6.50; $0
C. $5; $1.50
D. $5; $1.50
E. $1.50; $5
F. $1.50; $5
G. $0; $6.50
H. $0; $6.50
Answer: C. $5; $1.50
Intrinsic value = Max (0, 50 - 45) = $5
Time value = Call premium - Intrinsic value = $6.50 - $5 = $1.50
11. A 45 put option on a stock priced at $50 is priced at $3.50. This call has an intrinsic value
of ______ and a time value of _____.
A. $3.50; $0
B. $5; $3.50
C. $3.50; $5
D. $0; $3.50
Answer: D. $0; $3.50
Intrinsic value = Max(0, 45 - 50) = $0
Time value = Call premium - Intrinsic value = $3.50 - $0 = $3.50
12. Investor A bought a call option that expires in 6 months. Investor B wrote a put option
with a 9-month maturity. All else equal, as the time to expiration approaches, the value of
investor A's position will _______ and the value of investor B's position will _______.
A. increase; increase
B. increase; decrease
C. decrease; increase
D. decrease; decrease
Answer: C. decrease; increase
13. Investor A bought a call option, and investor B bought a put option. All else equal, if the
interest rate increases, the value of investor A's position will ______ and the value of investor
B's position will _______.
A. increase; increase
B. increase; decrease
C. decrease; increase
D. decrease; decrease
Answer: B. increase; decrease
14. Investor A bought a call option, and investor B bought a put option. All else equal, if the
underlying stock price volatility increases, the value of investor A's position will ______ and
the value of investor B's position will _______.
A. increase; increase
B. increase; decrease
C. decrease; increase
D. decrease; decrease
Answer: A. increase; increase
15. The percentage change in the call option price divided by the percentage change in the
stock price is the __________ of the option.
A. delta
B. elasticity
C. gamma
D. theta
Answer: B. elasticity
16. Before expiration, the time value of an out-of-the-money stock option is __________.
A. equal to the stock price minus the exercise price
B. equal to zero
C. negative
D. positive
Answer: D. positive
17. The intrinsic value of a call option is equal to _______________.
A. the stock price minus the exercise price
B. the exercise price minus the stock price
C. the stock price minus the exercise price plus any expected dividends
D. the exercise price minus the stock price plus any expected dividends
Answer: A. the stock price minus the exercise price
18. The divergence between an option's intrinsic value and its market value is usually greatest
when ___________________.
A. the option is deep in the money
B. the option is approximately at the money
C. the option is far out of the money
D. time to expiration is very low
Answer: B. the option is approximately at the money
19. The value of a call option increases with all of the following except ___________.
A. stock price
B. time to maturity
C. volatility
D. dividend yield
Answer: D. dividend yield
20. The value of a put option increases with all of the following except ___________.
A. stock price
B. time to maturity
C. volatility
D. dividend yield
Answer: A. stock price
21. Perfect dynamic hedging requires _______________.
A. a smaller capital outlay than static hedging
B. less commission expense than static hedging
C. daily rebalancing
D. continuous rebalancing
Answer: D. continuous rebalancing
22. The delta of an option is __________.
A. the change in the dollar value of an option for a dollar change in the price of the underlying
asset
B. the change in the dollar value of the underlying asset for a dollar change in the call price
C. the percentage change in the value of an option for a 1% change in the value of the
underlying asset
D. the percentage change in the value of the underlying asset for a 1% change in the value of
the call
Answer: A. the change in the dollar value of an option for a dollar change in the price of the
underlying asset
23. If you know that a call option will be profitably exercised, then the Black-Scholes model
price will simplify to _______.
A. S0 - X
B. X - S0
C. S0 - PV(X)
D. PV(X) - S0
Answer: C. S0 - PV(X)
24. Hedge ratios for long calls are always __________.
A. between -1 and 0
B. between 0 and 1
C. 1
D. greater than 1
Answer: B. between 0 and 1
25. Which of the following is a true statement?
A. The actual value of a call option is greater than its intrinsic value prior to expiration.
B. The intrinsic value of a call option is always greater than its time value prior to expiration.
C. The intrinsic value of a call option is always positive prior to expiration.
D. The intrinsic value of a call option is greater than its actual value prior to expiration.
Answer: A. The actual value of a call option is greater than its intrinsic value prior to
expiration.
26. A longer time to maturity will unambiguously increase the value of a call option because:
I. The longer maturity time reduces the effect of a dividend on call price.
II. With a longer time to maturity the present value of the exercise price falls.
III. With a longer time to maturity the range of possible stock prices at expiration increases.
A. I only
B. I and II only
C. II and III only
D. I, II, and III
Answer: C. II and III only
27. Strike prices of options are adjusted for ____________ but not for ____________.
A. dividends; stock splits
B. stock splits; cash dividends
C. exercise of warrants; stock splits
D. stock price movements; stock dividends
Answer: B. stock splits; cash dividends
28. A high dividend payout will ______ the value of a call option and ______ the value of a
put option.
A. increase; decrease
B. increase; increase
C. decrease; increase
D. decrease; decrease
Answer: C. decrease; increase
29. According to the Black-Scholes option-pricing model, two options on the same stock but
with different exercise prices should always have the same _________________.
A. price
B. expected return
C. implied volatility
D. maximum loss
Answer: C. implied volatility
30. When the returns of an option and stock are perfectly correlated as in a two-state binomial
option model, the hedge ratio must be equal to the ratio of ____________.
A. the range of the option outcomes to the range of the stock outcomes
B. the range of the stock outcomes to the range of the option outcomes
C. the standard deviation of the option returns to the standard deviation of the stock returns
D. the standard deviation of the stock returns to the standard deviation of the option returns
Answer: A. the range of the option outcomes to the range of the stock outcomes
31. The Black-Scholes hedge ratio for a long call option is equal to __________.
A. N(d1)
B. N(d2)
C. N(d1) - 1
D. N(d2) - 1
Answer: A. N(d1)
32. The Black-Scholes hedge ratio for a long put option is equal to __________.
A. N(d1)
B. N(d2)
C. N(d1) - 1
D. N(d2) - 1
Answer: C. N(d1) - 1
33. In a binomial option model with three subintervals, the probability that the stock price
moves up every possible time is _________.
A. 25%
B. 15.5%
C. 12.5%
D. 8%
Answer: C. 12.5%
With three subintervals there are 23 = 8 possible paths to the four possible terminal stock
prices. Three up moves would be one path out of the possible eight, so the probability of three
up moves is 1/8 = 12.5%.
34. In the Black-Scholes model, if an option is not likely to be exercised, both N(d1) and
N(d2) will be close to ______. If the option is definitely likely to be exercised, N(d 1) and
N(d2) will be close to ______.
A. 1; 0
B. 0; 1
C. -1; 1
D. 1; -1
Answer: B. 0; 1
35. In the Black-Scholes model, as the stock's price increases, the values of N(d1) and N(d2)
will _______ for a call and _______ for a put option.
A. increase; decrease
B. increase; increase
C. decrease; increase
D. decrease; decrease
Answer: A. increase; decrease
36. Research suggests that option-pricing models that allow for the possibility of
___________ provide more accurate pricing than does the basic Black-Scholes option-pricing
model.
I. early exercise
II. changing expected returns of the stock
III. time varying stock price volatility
A. II only
B. I and III only
C. II and III only
D. I, II, and III
Answer: B. I and III only
37. Research suggests that the performance of the Black-Scholes option-pricing model has
__________________.
A. improved in recent years
B. remained about the same over time
C. been deficient for stocks with high dividend payouts
D. varied widely over the years since 1973
Answer: C. been deficient for stocks with high dividend payouts
38. Research conducted by Rubinstein (1994) suggests that _______________ command a
disproportionately high time value.
A. out-of-the-money call options
B. out-of-the-money put options
C. in-the-money call options
D. in-the-money put options
Answer: B. out-of-the-money put options
39. Of the variables in the Black-Scholes OPM, the __________ is not directly observable.
A. price of the underlying asset
B. risk-free rate of interest
C. time to expiration
D. variance of the underlying asset return
Answer: D. variance of the underlying asset return
40. The practice of using options or dynamic hedging strategies to provide protection against
investment losses while maintaining upside potential is called _________.
A. trading on gamma
B. index optioning
C. portfolio insurance
D. index arbitrage
Answer: C. portfolio insurance
41. The delta of a put option on a stock is always __________.
A. between 0 and -1
B. between -1 and 1
C. positive but less than 1
D. greater than 1
Answer: A. between 0 and -1
42. The price of a stock put option is __________ correlated with the stock price and
__________ correlated with the exercise price.
A. negatively; negatively
B. negatively; positively
C. positively; negatively
D. positively; positively
Answer: B. negatively; positively
43. The delta of a call option on a stock is always __________.
A. negative and less than -1
B. between -1 and 1
C. positive
D. positive but less than 1
Answer: D. positive but less than 1
44. Hedge ratios for long call positions are __________, and hedge ratios for long put
positions are ____________.
A. negative; negative
B. negative; positive
C. positive; negative
D. positive; positive
Answer: C. positive; negative
45. A higher-dividend payout policy will have a __________ impact on the value of a put and
a __________ impact on the value of a call.
A. negative; negative
B. negative; positive
C. positive; negative
D. positive; positive
Answer: C. positive; negative
46. A one-dollar increase in a stock's price would result in __________ in the call option's
value of __________ than one dollar.
A. a decrease; less
B. a decrease; more
C. an increase; less
D. an increase; more
Answer: C. an increase; less
47. A hedge ratio of .70 implies that a hedged portfolio should consist of ________.
A. long .70 calls for each short stock
B. long .70 shares for each long call
C. long .70 shares for each short call
D. short .70 calls for each long stock
Answer: C. long .70 shares for each short call
48. If a stock price increases, the price of a put option on the stock will __________ and the
price of a call option on the stock will __________.
A. decrease; decrease
B. decrease; increase
C. increase; decrease
D. increase; increase
Answer: B. decrease; increase
49. The current stock price of Alcoa is $70, and the stock does not pay dividends. The
instantaneous risk-free rate of return is 6%. The instantaneous standard deviation of Alcoa's
stock is 40%. You want to purchase a call option on this stock with an exercise price of $75
and an expiration date 30 days from now. Based on the Black-Scholes OPM, the call option's
delta will be __________.
A. .28
B. .31
C. .62
D. .70
Answer: B. .31
50. The current stock price of Alcoa is $70, and the stock does not pay dividends. The
instantaneous risk-free rate of return is 6%. The instantaneous standard deviation of Alcoa's
stock is 40%. You want to purchase a put option on this stock with an exercise price of $75
and an expiration date 30 days from now. According to the Black-Scholes OPM, you should
hold __________ shares of stock per 100 put options to hedge your risk.
A. 30
B. 34
C. 69
D. 74
Answer: C. 69
51. The current stock price of International Paper is $69, and the stock does not pay
dividends. The instantaneous risk-free rate of return is 10%. The instantaneous standard
deviation of International Paper's stock is 25%. You want to purchase a call option on this
stock with an exercise price of $70 and an expiration date 73 days from now.
Using the Black-Scholes OPM, the call option should be worth __________ today.
A. $2.50
B. $2.94
C. $3.26
D. $3.50
Answer: C. $3.26
52. The current stock price of International Paper is $69, and the stock does not pay
dividends. The instantaneous risk-free rate of return is 10%. The instantaneous standard
deviation of International Paper's stock is 25%. You want to purchase a call option on this
stock with an exercise price of $70 and an expiration date 73 days from now.
Using the Black-Scholes OPM, the put option should be worth __________ today.
A. $1.50
B. $2.88
C. $2.55
D. $3.00
Answer: B. $2.88
53. The current stock price of Johnson & Johnson is $64, and the stock does not pay
dividends. The instantaneous risk-free rate of return is 5%. The instantaneous standard
deviation of J&J's stock is 20%. You want to purchase a call option on this stock with an
exercise price of $55 and an expiration date 73 days from now.
Using the Black-Scholes OPM, the call option should be worth __________ today.
A. $.01
B. $.08
C. $9.26
D. $9.62
Answer: D. $9.62
54. The current stock price of Johnson & Johnson is $64, and the stock does not pay
dividends. The instantaneous risk-free rate of return is 5%. The instantaneous standard
deviation of J&J's stock is 20%. You want to purchase a call option on this stock with an
exercise price of $55 and an expiration date 73 days from now.
Using the Black-Scholes OPM, the put option should be worth __________ today.
A. $.01
B. $.07
C. $9.26
D. $9.62
Answer: B. $.07
55. The stock price of Ajax Inc. is currently $105. The stock price a year from now will be
either $130 or $90 with equal probabilities. The interest rate at which investors can borrow is
10%. Using the binomial OPM, the value of a call option with an exercise price of $110 and
an expiration date 1 year from now should be worth __________ today.
A. $11.59
B. $15
C. $20
D. $40
Answer: A. $11.59
Buying the stock and borrowing the present value of $90 will give the same payoff as (1/.50)
calls.
56. The stock price of Bravo Corp. is currently $100. The stock price a year from now will be
either $160 or $60 with equal probabilities. The interest rate at which investors invest in
riskless assets is 6%. Using the binomial OPM, the value of a put option with an exercise
price of $135 and an expiration date 1 year from now should be worth __________ today.
A. $34.09
B. $37.50
C. $38.21
D. $45.45
Answer: C. $38.21
Selling the stock and buying a 1-year discounted note with a $160 face value will give the
same payoff as investing in (1/.75) puts.
57. If you have an extremely "bullish" outlook on the stock market, you could attempt to
maximize your rate of return by ________________.
A. purchasing out-of-the-money call options
B. purchasing at-the-money bull spreads
C. purchasing in-the-money call options
D. purchasing at-the-money call options
Answer: A. purchasing out-of-the-money call options
58. Which one of the following will increase the value of a put option?
A. A decrease in the exercise price
B. A decrease in time to expiration of the put
C. An increase in the volatility of the underlying stock
D. An increase in stock price
Answer: C. An increase in the volatility of the underlying stock
59. You find the option prices for three June call options on the same stock. The 95 call has an
implied volatility of 25%, the 100 call has an implied volatility of 25%, and the 105 call has
an implied volatility of 30%. If you believe this represents a mispricing situation. you may
want to ____________________________.
A. buy the 105 call and write the 100 call
B. buy the 105 call and write the 95 call
C. buy either the 95 or the 100 call and write the 105 call
D. write the 105 call and write either the 95 or the 100 call
Answer: C. buy either the 95 or the 100 call and write the 105 call
60. You are considering purchasing a call option with a strike price of $35. The price of the
underlying stock is currently $27. Without any further information, you would expect the
hedge ratio for this option to be _______________.
A. negative and near 0
B. negative and near -1
C. positive and near 0
D. positive and near 1
Answer: C. positive and near 0
61. According to the put-call parity theorem, the payoffs associated with ownership of a call
option can be replicated by __________________.
A. shorting the underlying stock, borrowing the present value of the exercise price, and
writing a put on the same underlying stock and with the same exercise price
B. buying the underlying stock, borrowing the present value of the exercise price, and buying
a put on the same underlying stock and with the same exercise price
C. buying the underlying stock, borrowing the present value of the exercise price, and writing
a put on the same underlying stock and with the same exercise price
D. shorting the underlying stock, lending the present value of the exercise price, and buying a
put on the same underlying stock and with the same exercise price
Answer: B. buying the underlying stock, borrowing the present value of the exercise price,
and buying a put on the same underlying stock and with the same exercise price
62. You are considering purchasing a put option on a stock with a current price of $33. The
exercise price is $35, and the price of the corresponding call option is $2.25. According to the
put-call parity theorem, if the risk-free rate of interest is 4% and there are 90 days until
expiration, the value of the put should be ____________.
A. $2.25
B. $3.91
C. $4.05
D. $5.52
Answer: B. $3.91
P = C - S0 + Xe-rT or P = 2.25 - 33 + (35)e-(.04)(90/365) = 3.91
63. The stock price of Atlantis Corp. is $43 today. The risk-free rate of return is 10%, and
Atlantis Corp. pays no dividends. A call option on Atlantis Corp. stock with an exercise price
of $40 and an expiration date 6 months from now is worth $5 today. A put option on Atlantis
Corp. stock with an exercise price of $40 and an expiration date 6 months from now should be
worth __________ today.
A. $.05
B. $.14
C. $2
D. $3.95
Answer: A. $.05
P = 5 - 43 + (40)e-(.01)(.5) = .0495
64. The stock price of Harper Corp. is $33 today. The risk-free rate of return is 6%, and
Harper Corp. pays no dividends. A put option on Harper Corp. stock with an exercise price of
$30 and an expiration date 73 days from now is worth $.95 today. A call option on Harper
Corp. stock with an exercise price of $30 and the same expiration date should be worth
__________ today.
A. $2.25
B. $3.14
C. $3.99
D. $4.31
Answer: D. $4.31
C = S0 - Xe-rT + P; C = 33 - (30)e-(.06)(.2) + .95 = 4.308
65. A call option on Juniper Corp. stock with an exercise price of $75 and an expiration date 1
year from now is worth $3 today. A put option on Juniper Corp. stock with an exercise price
of $75 and an expiration date 1 year from now is worth $2.50 today. The risk-free rate of
return is 8%, and Juniper Corp. pays no dividends. The stock should be worth __________
today.
A. $69.73
B. $71.69
C. $73.12
D. $77.25
Answer: A. $69.73
S0 = C + Xe-rT - P; S0 = 3.00 + (75)e-(.08)(1) - 2.5 = 69.73
66. 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.
Suppose the desired put options with X = 50 were traded. What would be the hedge ratio for
the option?
A. -1
B. -.5
C. .5
D. 1
Answer: B. -.5
H = (C+ - C-)/(S+ - S-) = -5/10 = -.5
The hedge ratio is -.5.
67. 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.
Suppose the desired put options with X = 50 were traded. How much would it cost to
purchase?
A. $1.19
B. $2.38
C. $5
D. $3.33
Answer: A. $1.19
The hedge ratio is -.5. A portfolio comprising one share and two puts would provide a
guaranteed payoff of 55, with present value of 55/1.05 = 52.38. Therefore,
S + 2P = 52.38
50 + 2P = 52.38
P = 1.19
68. 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 would have been the cost of a protective put portfolio?
A. $48.81
B. $51.19
C. $52.38
D. $53.38
Answer: B. $51.19
The hedge ratio is -.5. A portfolio comprising one share and two puts would provide a
guaranteed payoff of 55, with present value of 55/1.05 = 52.38. Therefore,
S + 2P = 52.38
50 + 2P = 52.38
P = 1.19
The protective put strategy = 1 share + 1 put = 50 + 1.19 = 51.19
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
Answer: C. ½ share of stock and $26.19 in bills
The hedge ratio is -.5. A portfolio comprising one share and two puts would provide a
guaranteed payoff of 55, with present value of 55/1.05 = 52.38. Therefore,
S + 2P = 52.38
50 + 2P = 52.38
P = 1.19
The protective put strategy = 1 share + 1 put = 50 + 1.19 = 51.19
The goal is a portfolio with the same exposure to the stock as the protective put portfolio.
Since the hedge ratio is -.5, you hold 1 - .5 = .5 shares of stock. The cost is $25 for the ½
share of stock. You place your remaining funds, $26.19, in bills earning 5%.
The stock plus bills strategy duplicates the cost and payoff of the protective put strategy.
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
Answer: A. overvalued and should be written; low
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
Answer: A. Short 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
Answer: A. 10
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
Answer: B. Early exercise
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
Answer: B. $2.22
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, riskfree rate = 2.5%, standard deviation = 22%, dividend yield = 8%.
A. $1.49
B. $1.79
C. $2.04
D. $2.19
Answer: C. $2.04
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
Answer: C. is zero
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
Answer: C. $4
Intrinsic value = 34 - 30 = 4
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. $.75
C. $1.50
D. $2.25
Answer: B. $.75
Time value = 2.25 - 1.50 = .75.
79. What aspect of the time value of money does the factor of e represent in the BlackScholes option value formula?
A. Annual compounding
B. Compounding at the expiration time frame
C. Continuous compounding
D. Daily compounding
Answer: C. Continuous 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
Answer: A. S0 - Xe-rt
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
Answer: C. write the call and buy the put and buy the stock and borrow the present value of
the exercise price
For parity to hold, the following condition must be met: C - P = S0 - Xe-rT
Buy what's underpriced (the left side of the equation) and sell what's overpriced (the right side
of the equation)
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. $.96
D. $.42
Answer: D. $.42
The arbitrage profit is the difference between the income from C - P and the cost of buying
the stock and borrowing the present value of the exercise price:
(C - P) - (S0 - Xe-rt) = (7.27 - 1.10) - (65 - 59.25467) = .42
The table below shows the cash flows.
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
Answer: B. stock prices may fall by a larger amount than the model assumes
84. A put option has a strike price of $35 and a stock price of $38. If the call option is trading
at $1.25, what is the time value embedded in the option?
A. $0
B. $.75
C. $1.25
D. $3
Answer: C. $1.25
Since the put option is out of money, intrinsic value is zero and option premium = time value.
85. Hedge ratios for long puts are always __________.
A. between -1 and 0
B. between 0 and 1
C. 1
D. greater than 1
Answer: A. between -1 and 0
Test Bank for Essentials of Investments
Zvi Bodie, Alex Kane, Alan Marcus
9780078034695, 9789389957877, 9781264140251, 9781260316148, 9780073382401, 9780078034695, 9781260013924, 9780077835422
