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# fm9 4 - The present value of \$10.40 at the daily compounded...

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Answers and Solutions: 9 - 4 9-7 The stock’s range of payoffs in six months is \$18 - \$13 = \$5. At expiration, the option will be worth \$18 - \$14 = \$4 if the stock price is \$18, and zero if the stock price \$13. The range of payoffs for the stock option is \$4 – 0 = \$5. Equalize the range to find the number of shares of stock: Option range / Stock range = \$4/\$5 = 0.8. With 0.8 shares, the stock’s payoff will be either 0.8(\$18) = \$14.40 or 0.8(\$13) = \$10.40. The portfolio’s payoff will be \$14.4 - \$4 = \$10.40, or \$10.40 – 0 = \$10.40.
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Unformatted text preview: The present value of \$10.40 at the daily compounded risk-free rate is: PV = \$10.40 / (1+ (0.06/365)) 365/2 = \$10.093. The option price is the current value of the stock in the portfolio minus the PV of the payoff: V = 0.8(\$15) - \$10.093 = \$1.907 ≈ .\$1.91. SOLUTION TO SPREADSHEET PROBLEMS 9-8 The detailed solution for the problem is available in the file Solution for FM12 Ch 09 P08 Build a Model.xls on the textbook’s web site....
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