PRIN.OF CORPORATE FINANCE
13th Edition
ISBN: 9781260013900
Author: BREALEY
Publisher: RENT MCG
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Textbook Question
Chapter 21, Problem 29PS
Option risk In Section 21-1, we used a simple one-step model to value two Amazon options each with an exercise price of $900. We showed that the call option could be replicated by borrowing $407.06 and investing $490.91 in .54545 share of Amazon stock. The put option could be replicated by selling short $409.10 of Amazon stock and lending $488.46.
- a. If the beta of Amazon stock is 1.5, 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 Amazon. What would be the beta of your portfolio now?
- e. Your answers to parts (c) and (d) should be the same. Explain.
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Consider a European call on Amazon Stock (AMZN) that expires in one period. The current stock
price is $100, the strike price is $120, and the risk-free rate is 5%. Assume AMZN stock will either
go up to $140 or down to $80. Construct a replicating portfolio using shares of AMZN stock and a
position in a risk-free asset ... what is the value of the call option?
Call Option Price = $4.84
Call Option Price = $2.95
Call Option Price = $7.93
Call Option Price = $12.04
You are pricing options with the following characteristics:
•Current stock price (St): $35.60
•Exercise price (X): $50
•Time to expiration (T-t): 9 months
•Risk-free rate (rf): 3.25%
•Volatility (0): 45%
(a): What is the Black-Scholes value of call option? In your hand-written solution, provide the calculations of
d1,d2, and the final call price. Use Excel or another spreadsheet program to compute the values of N(d1) and
N(d2). See the notes for details.
(b): Using put-call parity, what is the value of a put option? For this case, assume continuous compounding,
which implies that PVt(X)=e-r(T-t).X.
Suppose you construct a strategy based on options on a stock that is currently selling for $100. The strategy is as follows:
Buy one call option having an exercise price of $95.
Sell two calls having an exercise price of $100.
Buy one call option having an exercise price of $105.
All of the options are written on the same stock and all have the same expiration date.
Compute the payoff (the dollars you receive) from this strategy at the expiration date for each of the following alternative stocks prices: $90, $95, $98, $100, $102, $105, and $110.
What additional information would be required to determine whether your strategy had been profitable?
What is the name of this strategy?
Chapter 21 Solutions
PRIN.OF CORPORATE FINANCE
Ch. 21 - Binomial model Over the coming year, Ragworts...Ch. 21 - Binomial model Imagine that Amazons stock price...Ch. 21 - Prob. 3PSCh. 21 - Binomial model Suppose a stock price can go up by...Ch. 21 - Prob. 6PSCh. 21 - Two-step binomial model Suppose that you have an...Ch. 21 - Prob. 8PSCh. 21 - Option delta a. Can the delta of a call option be...Ch. 21 - Option delta Suppose you construct an option hedge...Ch. 21 - BlackScholes model Use the BlackScholes formula to...
Ch. 21 - Option risk A call option is always riskier than...Ch. 21 - Option risk a. In Section 21-3, we calculated the...Ch. 21 - Prob. 16PSCh. 21 - Prob. 18PSCh. 21 - American options The price of Moria Mining stock...Ch. 21 - American options Suppose that you own an American...Ch. 21 - American options Recalculate the value of the...Ch. 21 - American options The current price of the stock of...Ch. 21 - American options Other things equal, which of...Ch. 21 - Option exercise Is it better to exercise a call...Ch. 21 - Option delta Use the put-call parity formula (see...Ch. 21 - Option delta Show how the option delta changes as...Ch. 21 - Dividends Your company has just awarded you a...Ch. 21 - Option risk Calculate and compare the risk (betas)...Ch. 21 - Option risk In Section 21-1, we used a simple...Ch. 21 - Prob. 30PS
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