Question

Solve for the Black-Scholes price for a call option of a stock with a current price of $100 and standard deviation of 30 percent per year. The option’s exercise price is $110, and it expires in 1 year. The risk-free rate is 3 percent per year

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 =		110
r = Risk free rate =		3.0%
q = Dividend Yield =		0%
σ = Std dev =		30%
d1 = (ln(S/K)+(r-q+σ^2/2)*t)/(σ*t^(1/2)
d1 = (ln(100/110)+(0.03-0+0.3^2/2)*1)/(0.3*1^(1/2))
d1 = -0.067701
d2 = d1-σ*t^(1/2)
d2 =-0.067701-0.3*1^(1/2)
d2 = -0.367701
N(d1) = Cumulative standard normal dist. of d1
N(d1) =0.473012
N(d1) = Cumulative standard normal dist. of d2
N(d2) =0.356548
Value of call= 100*0.473012-0.356548*110*e^(-0.03*1)
Value of call= 9.24