CHAPTER 21

# Thenifinvestorsarerisk neutral p1001p050010 p04

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Unformatted text preview: s certain not to be exercised, it is valueless, regardless of the change in the stock price. d. If the stock price is \$110 at 6 months, the option delta is 0.33. Therefore, in order to replicate the stock, we buy three calls and lend, as follows: Initial Outlay Buy 3 calls ­60 Lend PV(55) ­50 ­110 This strategy Is equivalent to: Buy stock ­110 Stock Price = 55 0 +55 +55 +55 Stock Price = 220 165 +55 +220 +220 6. a. Yes, it is rational to consider the early exercise of an American put option. b. The possible prices of Buffelhead stock and the associated American put option values (shown in parentheses) are: Let p equal the probability of a rise in the stock price. Then, if investors are risk­ neutral: p (1.00) + (1 ­ p)(­0.50) = 0.10 p = 0.4 If the stock price in month 6 is \$110, and if the American put option is not exercised, it will be worth: [(0.4 ´ 0) + (0.6 ´ 165)]/1.10 = \$90 On the other hand, if it is exercised after 6 months, it is worth \$110. Thus, the investor should exercise the put early. Similarly, if the stock price in month 6 is \$440, and if the American put option is not exercised, it will be worth: [(0.4 ´ 0) + (0.6 ´ 0)]/1.10 = \$0 On the other hand, if it is exercised after 6 months, it will cost the investor \$220. The investor s...
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