Question

What is the price of a European put option on a non-dividend-paying stock when the stock price is $69, the strike price is $70, the risk-free interest rate is 5% per annum, the volatility is 35% per annum, and the time to maturity is six months?

Answer 1

As per Black Scholes Model
Value of put option = N(-d2)*K*e^(-r*t)-(S)*N(-d1)
Where
S = Current price =		69
t = time to expiry =		0.5
K = Strike price =		70
r = Risk free rate =		5.0%
q = Dividend Yield =		0%
σ = Std dev =		35%
d1 = (ln(S/K)+(r-q+σ^2/2)*t)/(σ*t^(1/2)
d1 = (ln(69/70)+(0.05-0+0.35^2/2)*0.5)/(0.35*0.5^(1/2))
d1 = 0.16662
d2 = d1-σ*t^(1/2)
d2 =0.16662-0.35*0.5^(1/2)
d2 = -0.080867
N(-d1) = Cumulative standard normal dist. of -d1
N(-d1) =0.433835
N(-d2) = Cumulative standard normal dist. of -d2
N(-d2) =0.532226
Value of put= 0.532226*70*e^(-0.05*0.5)-69*0.433835
Value of put= 6.4