Chapter 5: Q28I (page 555)
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?.
As N(d1) approaches 1.0, the put’s hedge ratio[N(d1) - 1]
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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.
You are very bullish (optimistic) on stock EFG, much more so than the rest of the market.
In each question, choose the portfolio strategy that will give you the biggest dollar profit if your bullish forecast turns out to be correct. Explain your answer.
a. Choice A: \(100,000 invested in calls with X = 50.
Choice B: \)100,000 invested in EFG stock.
b. Choice A: 10 call options contracts (for 100 shares each), with X = 50.
Choice B: 1,000 shares of EFG stock.
An investor buys a call at a price of \(4.50 with an exercise price of \)40. At what stock price will the investor break even on the purchase of the call?
Return to Example 16.1. Use the binomial model to value a one-year European put option with exercise price $110 on the stock in that example. Does your solution for the put price satisfy put-call parity?
a. A butterfly spread is the purchase of one call at exercise price X 1, the sale of two calls at exercise price X 2 , and the purchase of one call at exercise price X 3 . X 1 is less than X 2 , and X 2 is less than X 3 by equal amounts, and all calls have the same expiration date. Graph the payoff diagram to this strategy.
b. A vertical combination is the purchase of a call with exercise price X 2 and a put with exercise price X 1, with X 2 greater than X 1 . Graph the payoff to this strategy.
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