Chapter 5: Q1B (page 552)
A call option with a strike price of \(50 on a stock selling at \)55 costs $6.50. What are the call option’s intrinsic and time values?
Answer
$5 and $1.50
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Show that Black-Scholes call option hedge ratios increase as the stock price increases. Consider a one-year option with exercise price \(50 on a stock with annual standard deviation 20%. The T-bill rate is 3% per year. Find N (d1) for stock prices \)45, \(50, and \)55.
Suppose you think FedEx stock is going to appreciate substantially in value in the next year. Say the stock’s current price, S 0, is \(100, and the call option expiring in one year has an exercise price, X, of \)100 and is selling at a price, C, of \(10. With \)10,000 to invest, you are considering three alternatives:
a. Invest all \(10,000 in the stock, buying 100 shares.
b. Invest all \)10,000 in 1,000 options (10 contracts).
c. Buy 100 options (one contract) for \(1,000 and invest the remaining \)9,000 in a money market fund paying 4% interest annually.
What is your rate of return for each alternative for four stock prices one year from now?
Summarize your results in the table and diagram below.
Joan Tam, CFA, believes she has identified an arbitrage opportunity for a commodity as indicated by the information given in the following exhibit:
a. Describe the transactions necessary to take advantage of this specific arbitrage opportunity.
b. Calculate the arbitrage profit.
Should the rate of return of a call option on a long-term Treasury bond be more or less sensitive to changes in interest rates than the rate of return of the underlying bond?
All else being equal, is a put option on a high-beta stock worth more than one on a lowbetastock? The firms have identical firm-specific risk.
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