CHAPTER 21

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Unformatted text preview: s: Therefore, it is preferable to exercise the call. The value of the call in month 0 is: 5. a. The possible prices of Buffelhead stock and the associated call option values (shown in parentheses) are: Let p equal the probability of a rise in the stock price. Then, if investors are risk­neutral: p (1.00) + (1 ­ p)(­0.50) = 0.10 p = 0.4 If the stock price in month 6 is $110, then the option will not be exercised so that it will be worth: [(0.4 ´ 55) + (0.6 ´ 0)]/1.10 = $20 Similarly, if the stock price is $440 in month 6, then, if it is exercised, it will be worth ($440 ­ $165) = $275. If the option is not exercised, it will be worth: [(0.4 ´ 715) + (0.6 ´ 55)]/1.10 = $290 Therefore, the call option will not be exercised, so that its value today is: [(0.4 ´ 290) + (0.6 ´ 20)]/1.10 = $116.36 b. (i) If the price rises to $440: (ii) If the price falls to $110: c. The option delta is 1.0 when the call is certain to be exercised and is zero when it is certain not to be exercised. If the call is certain to be exercised, it is equivalent to buying the stock with a partly deferred payment. So a one­dollar change in the stock price must be matched by a one­dollar change in the option price. At the other extreme, when the call i...
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