Question

# 1. Calculate the value of the D1 parameter for a call option in the Black-Scholes model,...

1. Calculate the value of the D1 parameter for a call option in the Black-Scholes model, given the following information: Current stock price: \$65.70 Option strike price: \$74 Time to expiration: 7 months Continuously compounded annual risk-free rate: 3.79% Standard deviation of stock return: 22%

2. Calculate the value of the D2 parameter for a call option in the Black-Scholes model, given the following information: Current stock price: \$126.77 Option strike price: \$132 Time to expiration: 6 months Continuously compounded annual risk-free rate: 1.41%; Standard deviation of stock return: 25%

1

 S = Current price = 65.7 t = time to expiry = 0.583333333 K = Strike price = 74 r = Risk free rate = 3.8% q = Dividend Yield = 0% σ = Std dev = 22% d1 = (ln(S/K)+(r-q+σ^2/2)*t)/(σ*t^(1/2) d1 = (ln(65.7/74)+(0.0379-0+0.22^2/2)*0.583333333333333)/(0.22*0.583333333333333^(1/2)) d1 = -0.492426

2

 S = Current price = 126.77 t = time to expiry = 0.5 K = Strike price = 132 r = Risk free rate = 1.4% q = Dividend Yield = 0% σ = Std dev = 25% d1 = (ln(S/K)+(r-q+σ^2/2)*t)/(σ*t^(1/2) d1 = (ln(126.77/132)+(0.0141-0+0.25^2/2)*0.5)/(0.25*0.5^(1/2)) d1 = -0.100423 d2 = d1-σ*t^(1/2) d2 =-0.100423-0.25*0.5^(1/2) d2 = -0.2772

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