Chapter 21 Valuing Options 571
bre44380_ch21_547-572.indd 571 10/09/15 09:27 PM
- Option risk In Section 21-1 we used a simple one-step model to value two Google options
each with an exercise price of $530. We showed that the call option could be replicated by
borrowing $233.22 and investing $294.44 in .556 shares of Google stock. The put option
could be replicated by selling short $235.56 of Google stock and lending $291.52.
a. If the beta of Google stock is 1.15, what is the beta of the call according to the one-step model?
b. What is the beta of the put?
c. Suppose that you were to buy one call and invest the present value of the exercise price in
a bank loan. What would be the beta of your portfolio?
d. Suppose instead that you were to buy one share and one put option of Google. What would
be the beta of your portfolio now?
e. Your answers to parts (c) and (d ) should be the same. Explain.
- Option maturity Some corporations have issued perpetual warrants. Warrants are call
options issued by a firm, allowing the warrant holder to buy the firm’s stock.
a. What does the Black–Scholes formula predict for the value of an infinite-lived call option
on a non-dividend-paying stock? Explain the value you obtain. (Hint: What happens to the
present value of the exercise price of a long-maturity option?)
b. Do you think this prediction is realistic? If not, explain carefully why. (Hints: What about
dividends? What about bankruptcy?)
Look at the stocks listed in Table 7.3. Pick at least three stocks and find call option prices for
each of them on finance.yahoo.com. Now find monthly adjusted prices and calculate the stan-
dard deviation from the monthly returns using the Excel function STDEV.P. Convert the standard
deviation from monthly to annual units by multiplying by the square root of 12.
a. For each stock pick a traded option with a maturity of about six months and an exercise
price equal to the current stock price. Use the Black–Scholes formula and your estimate of
standard deviation to value each option. If the stock pays dividends, remember to subtract
from the stock price the present value of any dividends that the option holder will miss out
on. How close is your calculated value to the traded price of the option?
b. Your answer to part (a) will not exactly match the traded price. Experiment with differ-
ent values for the standard deviation until your calculated values match the prices of the
traded options as closely as possible. What are these implied volatilities? What do the
implied volatilities say about investors’ forecasts of future volatility?
● ● ● ● ●
FINANCE ON
THE WEBMINI-CASE ● ● ● ● ●
Bruce Honiball’s Invention
It was another disappointing year for Bruce Honiball, the manager of retail services at the Gibb
River Bank. Sure, the retail side of Gibb River was making money, but it didn’t grow at all in
- Gibb River had plenty of loyal depositors, but few new ones. Bruce had to figure out some
new product or financial service—something that would generate some excitement and attention.
Bruce had been musing on one idea for some time. How about making it easy and safe for Gibb
River’s customers to put money in the stock market? How about giving them the upside of invest-
ing in equities—at least some of the upside—but none of the downside?