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Options Solutions 12

Options Solutions 12 - Equalize the range to find the...

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Old Exam Problems - Options - Solutions Page 12 of 13 Pages 16. Assume that the current price of a stock is \$22, that in one year the price will be either \$27 or \$17, and that the annual risk-free rate is 6 percent. Given this information, determine the price of a call option on the stock that has an exercise price of \$22 and that expires in one year. A. \$0.98 B. \$1.98 * C. \$2.98 D. \$3.98 E. \$4.98 C u = \$27 - \$22 = \$5 C d = \$17 - \$22 = \$0 u = 1.2273 d = 0.7727 P = (1.06 - 0.7727) / (1.2273 - 0.7727) = 0.2873 / .4546 = .632 (1 - P) = .368 C 0 = [(\$5)(.632) + (\$0)(.368)] / 1.06 = \$2.98 Alternatively, The stock’s range of payoffs in one year is \$27 - \$17 = \$10. At expiration, the option will be worth \$27 - \$22 = \$5 if the stock price is \$27, and zero if the stock price \$17. The range of payoffs for the stock option is \$5 – 0 = \$5.
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Unformatted text preview: Equalize the range to find the number of shares of stock: Option range / Stock range = \$5/\$10 = 0.5. With 0.5 shares, the stock’s payoff will be either \$13.5 or \$8.5. The portfolio’s payoff will be \$13.5 - \$5 = \$8.5, or \$8.5 - 0 = \$8.5. The present value of \$8.5 at the risk-free rate is: PV = \$8.5 / (1.06) = \$8.02 The option price is the current value of the stock in the portfolio minus the PV of the payoff: C = 0.5(\$22) - \$8.02 = \$2.98 17. The current price of a stock is \$50 and the annual risk-free rate is 6 percent. A call option with an exercise price of \$55 and one year until expiration has a current value of \$7.20. Using the concept of put-call parity, determine the value of a put option written...
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