Question

Week 15_CH.21&22 A Saved Help Save & Exit Submit Check my work Problem 21-12 Use the Black-Scholes formula for the following stock: 50 points eBook Time to expiration Standard deviation Exercise price Stock price Annual interest rate Dividend 6 months 55% per year $51 $49 Print 58 0 References Calculate the value of a put option. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Value of a put optionſ

Answer 1

As per Black Scholes Model
Value of put option = N(-d2)*K*e^(-r*t)-(S)*N(-d1)
Where
S = Current price =		49
t = time to expiry =		0.5
K = Strike price =		51
r = Risk free rate =		5.0%
q = Dividend Yield =		0%
σ = Std dev =		55%
d1 = (ln(S/K)+(r-q+σ^2/2)*t)/(σ*t^(1/2)
d1 = (ln(49/51)+(0.05-0+0.55^2/2)*0.5)/(0.55*0.5^(1/2))
d1 = 0.155871
d2 = d1-σ*t^(1/2)
d2 =0.155871-0.55*0.5^(1/2)
d2 = -0.233038
N(-d1) = Cumulative standard normal dist. of -d1
N(-d1) =0.438067
N(-d2) = Cumulative standard normal dist. of -d2
N(-d2) =0.592134
Value of put= 0.592134*51*e^(-0.05*0.5)-49*0.438067
Value of put= 7.99