Chapter 5: Q15-28I (page 516)
Devise a portfolio using only call options and shares of stock with the following value (payoff ) at the option expiration date. If the stock price is currently $53, what kind of bet is the investor making?
Volatility bet
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The common stock of the C.A.L.L. Corporation has been trading in a narrow range around \(50 per share for months, and you believe it is going to stay in that range for the next three months. The price of a three-month put option with an exercise price of \)50 is \(4, and a call with the same expiration date and exercise price sells for \)7.
a. What would be a simple options strategy using a put and a call to exploit your conviction about the stock price’s future movement?
b. What is the most money you can make on this position? How far can the stock price move in either direction before you lose money?
c. How can you create a position involving a put, a call, and riskless lending that would have the same payoff structure as the stock at expiration? The stock will pay no dividends in the next three months. What is the net cost of establishing that position now?
The Excel Applications box in the chapter (available at www.mhhe.com/bkm ; link to Chapter 17 material) shows how to use the spot-futures parity relationship to find a “term structure of futures prices,” that is, futures prices for various maturity dates.
a. Suppose that today is January 1, 2012. Assume the interest rate is 1% per year and a stock index currently at 1,200 pays a dividend yield of 2%. Find the futures price for contract maturity dates of February 14, 2012, May 21, 2012, and November 18, 2012.
b. What happens to the term structure of futures prices if the dividend yield is lower than the risk-free rate? For example, what if the interest rate is 3%?
According to the Black-Scholes formula, what will be the value of the hedge ratio of a put option for a very small exercise price?.
You are attempting to value a call option with an exercise price of \(100 and one year to expiration. The underlying stock pays no dividends, its current price is \)100, and you believe it has a 50% chance of increasing to \(120 and a 50% chance of decreasing to \)80.
The risk-free rate of interest is 10%. Calculate the call option’s value using the two-state stock price model.
Consider the following options portfolio: You write a January 2012 expiration calloption on IBM with exercise price \(170. You also write a January expiration IBM putoption with exercise price \)165.
a. Graph the payoff of this portfolio at option expiration as a function of IBM’s stockprice at that time.
b. What will be the profit/loss on this position if IBM is selling at \(167 on the optionexpiration date? What if IBM is selling at \)175? Use The Wall Street Journal listingfrom Figure 15.1 to answer this question.
c. At what two stock prices will you just break even on your investment?
d. What kind of “bet” is this investor making; that is, what must this investor believeabout IBM’s stock price in order to justify this position?
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