Question

The current stock price of Well-Tempered Flugelhorns (WTF) is $40 with an instantaneous standard deviation of 20%. If the risk-free rate is 3%, what is the value of a put option with an exercise price of $45 that expires in 6 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 =		45
t = time to expiry =		0.5
K = Strike price =		40
r = Risk free rate =		3.0%
q = Dividend Yield =		0%
σ = Std dev =		20%
d1 = (ln(S/K)+(r-q+σ^2/2)*t)/(σ*t^(1/2)
d1 = (ln(45/40)+(0.03-0+0.2^2/2)*0.5)/(0.2*0.5^(1/2))
d1 = 1.009629
d2 = d1-σ*t^(1/2)
d2 =1.009629-0.2*0.5^(1/2)
d2 = 0.868208
N(-d1) = Cumulative standard normal dist. of -d1
N(-d1) =0.156337
N(-d2) = Cumulative standard normal dist. of -d2
N(-d2) =0.19264
Value of put= 0.19264*40*e^(-0.03*0.5)-45*0.156337
Value of put= 0.56