Options Solutions 12

Options Solutions 12 - Equalize the range to find the number of shares of stock Option range Stock range = $5/$10 = 0.5 With 0.5 shares 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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This note was uploaded on 07/13/2011 for the course FIN 4414 taught by Professor Staff during the Spring '08 term at University of Florida.

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