Question

A non-dividend paying stock price is $100, the strike price is $100, the risk-free rate is 6%, the volatility is 15% and the time to maturity is 3 months which of the following is the price of an American Call option on the stock. For full credit I expect each step of the calculations tied to the correct formulas.

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 =		0.25
K = Strike price =		100
r = Risk free rate =		6.0%
q = Dividend Yield =		0.00%
σ = Std dev =		15%
d1 = (ln(S/K)+(r-q+σ^2/2)*t)/(σ*t^(1/2)
d1 = (ln(100/100)+(0.06-0+0.15^2/2)*0.25)/(0.15*0.25^(1/2))
d1 = 0.2375
d2 = d1-σ*t^(1/2)
d2 =0.2375-0.15*0.25^(1/2)
d2 = 0.1625
N(d1) = Cumulative standard normal dist. of d1
N(d1) =0.593866
N(d2) = Cumulative standard normal dist. of d2
N(d2) =0.564544
Value of call= 100*0.593866-0.564544*100*e^(-0.06*0.25)
Value of call= 3.77