Question

Black-Scholes Model Use the Black-Scholes Model to find the price for a call option with the following inputs: (1) Current stock price is $21. (2) Strike price is $24. (3) Time to expiration is 5 months. (4) Annualized risk-free rate is 4%. (5) Variance of stock return is 0.17. Round your answer to the nearest cent. In your calculations round normal distribution values to 4 decimal places.

Please show step by step calculations in excel. Thank you

Answer 1

std dev = variance^(1/2) = 0.17^(1/2)=41.23%

time to expiry =5/12 = 0.41666 years

As per Black Scholes Model
Value of call option = S*N(d1)-N(d2)*K*e^(-r*t)
Where
S = Current price =		21
t = time to expiry =		0.41666
K = Strike price =		24
r = Risk free rate =		4%
q = Dividend Yield =		0%
σ = Std dev =		41.23%
d1 = (ln(S/K)+(r-q+σ^2/2)*t)/(σ*t^(1/2)
d1 = (ln(21/24)+(0.04-0+0.4123^2/2)*0.41666)/(0.4123*0.41666^(1/2))
d1 = -0.306049
d2 = d1-σ*t^(1/2)
d2 =-0.306049-0.4123*0.41666^(1/2)
d2 = -0.572185
N(d1) = Cumulative standard normal dist. of d1
N(d1) =0.3798
N(d1) = Cumulative standard normal dist. of d2
N(d2) =0.2836
Value of call= 21*0.3798-0.2836*24*e^(-0.04*0.41666)
Value of call= 1.28