Question

Use the Black-Scholes model to find the price for a call option with the following inputs: (1) current stock price is $30, (2) strike price is $37, (3) time to expiration is 3 months, (4) annualized risk-free rate is 5%, and (5) variance of stock return is 0.16. Do not round intermediate calculations. Round your answer to the nearest cent.

$ ??????

PLEASE SHOW THE FORMULA!! Thank you :)

Answer 1

As per Black Scholes Model
Value of call option = (S)*N(d1)-N(d2)*K*e^(-r*t)
Where
S = Current price =		30
t = time to expiry =		0.25
K = Strike price =		37
r = Risk free rate =		5.0%
q = Dividend Yield =		0%
σ = Std dev =		40%
d1 = (ln(S/K)+(r-q+σ^2/2)*t)/(σ*t^(1/2)
d1 = (ln(30/37)+(0.05-0+0.4^2/2)*0.25)/(0.4*0.25^(1/2))
d1 = -0.886103
d2 = d1-σ*t^(1/2)
d2 =-0.886103-0.4*0.25^(1/2)
d2 = -1.086103
N(d1) = Cumulative standard normal dist. of d1
N(d1) =0.187781
N(d2) = Cumulative standard normal dist. of d2
N(d2) =0.138717
Value of call= 30*0.187781-0.138717*37*e^(-0.05*0.25)
Value of call= 0.56