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Options Solutions 6

Options Solutions 6 - Weekly = 52 Daily = 252 Annualized σ...

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Old Exam Problems - Options - Solutions Page 6 of 13 Pages * D. \$12.67 E. \$13.23 PV(EX) = \$50 / (e .04 ) = \$48.04 d 1 = {[LN(\$60 / \$48.04)] / (.20)(1)} + [(.20)(1)/2] = 1.21 d 2 = = 1.21 - (.20)(1) = 1.01 N(d 1 ) = .8869 N(d 2 ) = .8438 C 0 = (.8869)(\$60.00) - (.8438)(\$48.04) = \$53.21 - \$40.54 = \$12.67 8. Assume that you calculate the standard deviation of a security’s returns to be 5.04% using monthly data. Determine the annualized standard deviation of these returns using the method discussed in class with respect to the case Ito’s Dilemma. A. 18.23% * B. 17.46% C. 19.87% D. 16.59% E. 20.92% To annualize a standard deviation you simply take the periodic standard deviation and multiply by the square root of the number of periods within a year: Monthly = 12;
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Unformatted text preview: Weekly = 52; Daily = 252. Annualized σ = (Monthly σ )* (12) 1/2 = (0.0504)*(3.4641) = 17.46% 9. Assume that you have a call option with a strike (exercise) price of \$45, a current stock price of \$52, 146 days until expiration, and an annualized standard deviation of 28.24%. Assuming a risk-free rate of 4.00 percent, and using the cumulative probability tables provided at the end of this exam, determine the price of this call option using the Black-Scholes Option Pricing Formula. (Take all preliminary numbers out to 9 decimal places.) A. \$10.85 B. \$ 3.07 C. \$12.36 * D. \$ 8.59 E. \$ 5.92 PV (Exercise) = (\$45.00)*e-(.04)*(146/365) = \$44.29 d 1 = {[ln(\$52.00/\$44.29)] / (.2824)*(146/365) 1/2 } + [(.2824)*(146/365) 1/2 / 2]...
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