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Options Solutions 11 - • The risk-free rate is 6 percent...

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Old Exam Problems - Options - Solutions Page 11 of 13 Pages C uu = $135.20 - $75.00 = $60.20 C ud = $ 83.20 - $75.00 = $ 8.20 C du = $ 83.20 - $75.00 = $ 8.20 C dd = $ 51.20 - $75.00 = $ 0.00 C u = [(.42)($60.20) + (.58)($ 8.20)]/[1.01] = $29.74 C d = [(.42)($ 8.20) + (.58)($ 0.00)]/[1.01] = $ 3.41 C 0 = [(.42)($29.74) + (.58)($ 3.41)]/[1.01] = $14.33 15. Assume that an analyst is interested in using the Black-Scholes model to value call options on the stock of your company, and that the analyst has accumulated the following information: The price of the stock is $40 The strike price is $40 The option matures in 3 months (t = 0.25) The standard deviation of the stock’s returns is 0.40 and the variance is 0.16
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Unformatted text preview: • The risk-free rate is 6 percent Using the Black-Scholes model, determine the value of the call option. A. $0.60 B. $3.17 C. $4.20 D. $8.00 * E. $3.47 Given this information, the analyst is then able to calculate some other necessary components of the Black-Scholes model: • d 1 = 0.175 • d 2 = -0.025 • N(d 1 ) = 0.5695 • N(d 2 ) = 0.4900 N(d 1 ) and N(d 2 ) represent areas under a standard normal distribution function. The Black-Scholes model calculates the value of the call option as: V = P [N(d 1 )] - (X)e (RF)(t) [N(d 2 )] V = ($40)(0.5695)] - ($40)(e-(0.06)(0.25) )(0.4900) = $3.47...
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