D. Options have a unique set of terminology. Define the following
terms: (1) call option; (2) put option; (3) exercise price; (4)
striking, or strike, price; (5) option price; (6) expiration date; (7)
exercise value; (8) covered option; (9) naked option; (10) in-the-
money call; (11) out-of-the-money call; and (12) LEAPS.
Answer: [Show S18–5 through S18-7 here.]
A call option is an option to buy a specified number of shares of a
E. Consider Tropical Sweets’ call option with a $25 strike price. The
following table contains historical values for this option at different
stock prices:
Stock Price Call Option Price
$25 $ 3.00
30 7.50
35 12.00
40 16.50
45 21.00
50 25.50
(1) Create a table that shows the (a) stock price, (b) strike price, (c)
exercise value, (d) option price, and (e) premium of option price
over exercise value.
Answer: [Show S18–8 and S18-9 here.]
Price of
Stock
Strike
Price
Exercise Value
of Option
Market Price
of Option
Premium
(a)
(b)
(a) – (b) = (c)
(d)
(d) – (c) = (e)
$25.00
$25.00
$ 0.00
$ 3.00
$3.00
12.00
16.50
E. (2) What happens to the premium of option price over exercise value as
the stock price rises? Why?
Answer: [Show S18–10 and S18-11 here.] As the table shows, the premium
F. In 1973, Fischer Black and Myron Scholes developed the Black-
Scholes Option Pricing Model.
(1) What assumptions underlie this model?
Answer: [Show S18–12 here.] The assumptions that underlie the Black-
Scholes Option Pricing Model are as follows:
F. (2) Write the three equations that constitute the model.
Answer: [Show S18–13 here.] The Black–Scholes Option Pricing Model consists
of the following three equations:
Here,
F. (3) What is the value of the following call option according to this
model?
Stock price = $27.00.
Exercise price = $25.00.
Time to expiration = 6 months.
Risk-free rate = 6.0%.
Stock return variance = 0.11.
Answer: [Show S18–14 and S18-15 here.] The input variables are:
G. Disregard the information in part F. Determine the value of a firm’s
call option using the binomial approach by creating a riskless hedge
given the following information. A firm’s current stock price is $15
per share. Options exist that permit the holder to buy one share of
the firm’s stock at an exercise price of $15. These options expire in
6 months, at which time the firm’s stock will be selling at one of
two prices, $10 or $20. The risk-free rate is 6%. What is the value
of the firm’s call option?
Answer: [Show S18-16 through S18–19 here.]
H. What effect does each of the following call option parameters have
on the value of a call option? (1) Current stock price; (2) exercise
price; (3) length of the option period; (4) risk-free rate; (5)
variability of the stock price.
Answer: [Show S18-20 and S18-21 here.]
I. What are the differences between forward and futures contracts?
Answer: [Show S18-22 here.] Forward contracts are agreements where one
J. Explain briefly how swaps work.
Answer: [Show S18-23 here.] A swap is the exchange of cash payment
K. Explain briefly how a firm can use futures and swaps to hedge risk.
Answer: [Show S18-24 and S18-25 here.] Hedging is usually used when a
L. What is corporate risk management? Why is it important to all firms?
Answer: [Show S18–26 through S18-29 here.] Corporate risk management
Appendix 18A
Valuation of Put Options
Answer to Question
18A-1 The put-call parity relationship is explained by the following equation:
Solutions to Problems
18A-1 Put option = V – P +
trRF
Xe–
where V = value of the call option.
18A-2 Put option = V – P +
trRF
Xe–
where V = value of the call option.