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?
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 |
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