Question

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%

Answer 1

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