Question

Let S = $58, s = 29%, r = 6%, and d = 3% (continuously compounded). Compute the Black-Scholes price for a $50-strike European put option with 9 months until expiration.

Answer= $1.92

Please show all the work to get that answer.

Thanks

Answer 1

As per Black Scholes Model
Value of put option = N(-d2)*K*e^(-r*t)-S*N(-d1)*e^(-q*t)
Where
S = Current price =		58
t = time to expiry =		0.75
K = Strike price =		50
r = Risk free rate =		6.0%
q = Dividend Yield =		3%
σ = Std dev =		29%
d1 = (ln(S/K)+(r-q+σ^2/2)*t)/(σ*t^(1/2)
d1 = (ln(58/50)+(0.06-0.03+0.29^2/2)*0.75)/(0.29*0.75^(1/2))
d1 = 0.80613
d2 = d1-σ*t^(1/2)
d2 =0.80613-0.29*0.75^(1/2)
d2 = 0.554983
N(-d1) = Cumulative standard normal dist. of -d1
N(-d1) =0.210084
N(-d2) = Cumulative standard normal dist. of -d2
N(-d2) =0.289453
Value of put= 0.289453*50*e^(-0.06*0.75)-58*0.210084*e^(-0.03*0.75)
Value of put= 1.92