Chapter 21 – Option Valuation
21–20
55. Lower dividend payout policies have a __________ impact on the value of the call and a
__________ impact on the value of the put.
Difficulty: Moderate
56. A one dollar decrease in a call option’s exercise price would result in a(n) __________ in
the call option’s value of __________ one dollar.
Difficulty: Moderate
21–21
57. Which one of the following variables influence the value of call options?
I) Level of interest rates.
II) Time to expiration of the option.
III) Dividend yield of underlying stock.
IV) Stock price volatility.
Difficulty: Moderate
58. Which one of the following variables influence the value of put options?
I) Level of interest rates.
II) Time to expiration of the option.
III) Dividend yield of underlying stock.
IV) Stock price volatility.
Difficulty: Moderate
21–22
59. An American call option buyer on a non-dividend paying stock will
Difficulty: Moderate
60. Relative to European puts, otherwise identical American put options
Difficulty: Moderate
61. Use the two-state put option value in this problem. SO = $100; X = $120; the two
possibilities for ST are $150 and $80. The range of P across the two states is _____; the hedge
ratio is _______.
Difficulty: Difficult
21–23
62. Use the Black-Scholes Option Pricing Model for the following problem. Given: SO = $70;
X = $70; T = 70 days; r = 0.06 annually (0.0001648 daily); = 0.020506 (daily). No
dividends will be paid before option expires. The value of the call option is _______.
0.5600($70) – $70[e-(0.0001648)(70)]0.4919 = $5.16.
Difficulty: Difficult
63. Empirical tests of the Black-Scholes option pricing model
Difficulty: Difficult
21–24
64. Options sellers who are delta-hedging would most likely
65. What is the intrinsic value of the call?
Difficulty: Easy
66. What is the time value of the call?
Difficulty: Moderate
21–25
67. If the option has delta of .5, what is its elasticity?
Difficulty: Difficult
68. If the risk-free rate is 6%, what should be the value of a put option on the same stock with
the same strike price and expiration date?
Difficulty: Difficult
69. If the company unexpectedly announces it will pay its first-ever dividend 3 months from
today, you would expect that
Difficulty: Moderate
21–26
70. Since deltas change as stock values change, portfolio hedge ratios must be constantly
updated in active markets. This process is referred to as
Difficulty: Moderate
71. In volatile markets, dynamic hedging may be difficult to implement because
Difficulty: Easy
72. Rubinstein (1994) observed that the performance of the Black-Scholes model had
deteriorated in recent years, and he attributed this to
Difficulty: Moderate
21–27
73. The time value of a call option is
I) the difference between the option’s price and the value it would have if it were expiring
immediately.
II) the same as the present value of the option’s expected future cash flows.
III) the difference between the option’s price and its expected future value.
IV) different from the usual time value of money concept.
Difficulty: Easy
74. The time value of a put option is
I) the difference between the option’s price and the value it would have if it were expiring
immediately.
II) the same as the present value of the option’s expected future cash flows.
III) the difference between the option’s price and its expected future value.
IV) different from the usual time value of money concept.
Difficulty: Easy
21–28
75. You purchased a call option for a premium of $4. The call has an exercise price of $29
and is expiring today. The current stock price is $31. What would be your best course of
action?
Difficulty: Moderate
76. As the underlying stock’s price increased, the call option valuation function’s slope
approaches
Difficulty: Moderate
21–29
77. Relative to non-dividend-paying European calls, otherwise identical American call
options
Difficulty: Moderate
78. The Black-Scholes formula assumes that
I) the risk-free interest rate is constant over the life of the option.
II) the stock price volatility is constant over the life of the option.
III) the expected rate of return on the stock is constant over the life of the option.
IV) there will be no sudden extreme jumps in stock prices.
Difficulty: Difficult
21–30
79. Which Excel formula is used to execute the Black-Scholes option pricing model?
Difficulty: Easy
80. The hedge ratio of an option is also called the options _______.
Difficulty: Easy
81. Dollar movements in option prices are ________ than dollar movements in the stock
price, and rate of return volatility of options is ________ than stock return volatility.
Difficulty: Moderate
21–31
82. What is the intrinsic value of the call?
Difficulty: Easy
83. What is the time value of the call?
Difficulty: Moderate
21–32
84. If the company unexpectedly announces it will pay its first-ever dividend 4 months from
today, you would expect that
Difficulty: Moderate
Short Answer Questions
85. Discuss the relationship between option prices and time to expiration, volatility of the
underlying stocks, and the exercise price.
Difficulty: Moderate
21–33
86. Which of the variables affecting option pricing is not directly observable? If this variable
is estimated to be higher or lower than the variable actually is how is the option valuation
affected?
The volatility of the underlying stock is not directly observable, but can be estimated from
Difficulty: Difficult
87. What is an option hedge ratio? How does the hedge ratio for a call differ from that of a put
(or are the two equivalent)? Explain.
Difficulty: Moderate
21–34
88. You are evaluating a stock that is currently selling for $30 per share. Over the investment
period you think that the stock price might get as low as $25 or as high as $40. There is a call
option available on the stock with an exercise price of $35. Answer the following questions
about hedging your position in the stock. Assume that you will hold one share.
What is the hedge ratio?
How much would you borrow to purchase the stock?
What is the amount of your net investment in the stock?
Complete the table below to show the value of your stock portfolio at the end of the holding
period.
How many call options will you combine with the stock to construct the perfect hedge? Will
you buy the calls or sell the calls?
Show the option values in the table below.
Chapter 21 – Option Valuation
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What must the price of one call option be?
Chapter 21 – Option Valuation
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The answers are shown below.
What is the hedge ratio? The hedge ratio equals the range of the call values divided by the
range of the stock values, which equals (5 – 0)/(40 – 25) = 1/3. [If the stock price ends at $40
the call is worth $5; if it ends at $25 the call is worth $0.]
How much would you borrow to purchase the stock? Borrow the present value of the
anticipated minimum stock price = $25/1.06 = $23.58
What is the amount of your net investment in the stock? The net amount of investment is $30
– 23.58 = $6.42.
Complete the table below to show the value of your stock portfolio at the end of the holding
period.
How many call options will you combine with the stock to construct the perfect hedge? Will
you buy the calls or sell the calls? Since the hedge ratio is 1/3 buy one stock and sell three call
options.
Show the option values in the table below.
Chapter 21 – Option Valuation
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What must the price of one call option be? The value of the stock portfolio equals the value of
Difficulty: Difficult