Question

Compute the Black-Scholes price of a call. Suppose S=$100, K=$95, σ=30%, r=0.08, δ=0.03, and T=0.75.

Answer 1

As per Black Scholes Model
Value of call option = S*N(d1)-N(d2)*K*e^(-r*t)
Where
S = Current price =		100
t = time to expiry =		0.75
K = Strike price =		95
r = Risk free rate =		8.0%
q = Dividend Yield =		3.0%
σ = Std dev =		30%
d1 = (ln(S/K)+(r-q+σ^2/2)*t)/(σ*t^(1/2)
d1 = (ln(100/95)+(0.08-0.03+0.3^2/2)*0.75)/(0.3*0.75^(1/2))
d1 = 0.471669
d2 = d1-σ*t^(1/2)
d2 =0.471669-0.3*0.75^(1/2)
d2 = 0.211861
N(d1) = Cumulative standard normal dist. of d1
N(d1) =0.681419
N(d1) = Cumulative standard normal dist. of d2
N(d2) =0.583892
Value of call= 100*0.681419-0.583892*95*e^(-0.08*0.75)
Value of call= 15.9