Question

Use the Black-Scholes formula for the following stock: Time to expiration 6 months Standard deviation 46% per year Exercise price $48 Stock price $47 Annual interest rate 6% Dividend 0 Calculate the value of a call option. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer 1

As per Black Scholes Model
Value of call option = (S)*N(d1)-N(d2)*K*e^(-r*t)
Where
S = Current price =		47
t = time to expiry =		0.5
K = Strike price =		48
r = Risk free rate =		6.0%
q = Dividend Yield =		0%
σ = Std dev =		46%
d1 = (ln(S/K)+(r-q+σ^2/2)*t)/(σ*t^(1/2)
d1 = (ln(47/48)+(0.06-0+0.46^2/2)*0.5)/(0.46*0.5^(1/2))
d1 = 0.19014
d2 = d1-σ*t^(1/2)
d2 =0.19014-0.46*0.5^(1/2)
d2 = -0.135129
N(d1) = Cumulative standard normal dist. of d1
N(d1) =0.5754
N(d2) = Cumulative standard normal dist. of d2
N(d2) =0.446255
Value of call= 47*0.5754-0.446255*48*e^(-0.06*0.5)
Value of call= 6.26