Question

Astock trades for $45 per share. A call option on that stock has a strike price of $53 and an expiration date twelve months in the future. The volatility of the stock's returns is 37%, and the risk-free rate is 2%. What is the Black and Scholes value of this option? The Black and Scholes value of this call option is $ . (Round to the nearest cent.)

I answered wuestion 2 and 3. I just need the first question answered please.

stock trades question.

Answer 1

As per Black Scholes Model
Value of call option = (S)*N(d1)-N(d2)*K*e^(-r*t)
Where
S = Current price =		45
t = time to expiry =		1
K = Strike price =		53
r = Risk free rate =		2.0%
q = Dividend Yield =		0%
σ = Std dev =		37%
d1 = (ln(S/K)+(r-q+σ^2/2)*t)/(σ*t^(1/2)
d1 = (ln(45/53)+(0.02-0+0.37^2/2)*1)/(0.37*1^(1/2))
d1 = -0.203188
d2 = d1-σ*t^(1/2)
d2 =-0.203188-0.37*1^(1/2)
d2 = -0.573188
N(d1) = Cumulative standard normal dist. of d1
N(d1) =0.419494
N(d2) = Cumulative standard normal dist. of d2
N(d2) =0.283259
Value of call= 45*0.419494-0.283259*53*e^(-0.02*1)
Value of call= 4.16