Question

Let S = $100, K = $120, σ = 30%, r = 0.08, and δ = 0. Compute the Black-Scholes call price for 1 year to maturity.

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 =		1
K = Strike price =		120
r = Risk free rate =		8.0%
q = Dividend Yield =		0%
σ = Std dev =		30%
d1 = (ln(S/K)+(r-q+σ^2/2)*t)/(σ*t^(1/2)
d1 = (ln(100/120)+(0.08-0+0.3^2/2)*1)/(0.3*1^(1/2))
d1 = -0.191072
d2 = d1-σ*t^(1/2)
d2 =-0.191072-0.3*1^(1/2)
d2 = -0.491072
N(d1) = Cumulative standard normal dist. of d1
N(d1) =0.424235
N(d1) = Cumulative standard normal dist. of d2
N(d2) =0.311688
Value of call= 100*0.424235-0.311688*120*e^(-0.08*1)
Value of call= 7.9