Question

Let S = $100, K = $120, σ = 30%, r = 0.08, and δ = 0. Compute the Black-Scholes call price for 2 year to maturity with dividend yield of 0.001.

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 =		2
K = Strike price =		120
r = Risk free rate =		8.0%
q = Dividend Yield =		0.1%
σ = Std dev =		30%
d1 = (ln(S/K)+(r-q+σ^2/2)*t)/(σ*t^(1/2)
d1 = (ln(100/120)+(0.08-0.001+0.3^2/2)*2)/(0.3*2^(1/2))
d1 = 0.154806
d2 = d1-σ*t^(1/2)
d2 =0.154806-0.3*2^(1/2)
d2 = -0.269458
N(d1) = Cumulative standard normal dist. of d1
N(d1) =0.561513
N(d1) = Cumulative standard normal dist. of d2
N(d2) =0.393789
Value of call= 100*0.561513-0.393789*120*e^(-0.08*2)
Value of call= 15.88