Question

Consider a European put option on a currency. The exchange rate is $1.15 per unit of the foreign currency, the strike price is $1.25, the time to maturity is one year, the domestic risk-free rate is 0% per annum, and the foreign risk-free rate is 5% per annum. The volatility of the exchange rate is 0.25. What is the value of this put option according to the Black-Scholes-Merton model?

Answer 1

Value of put option = N(-d2)*K*e^(-Rd*t)-(S*e^(-Rf*t))*N(-d1)
Where
S = Current price =		1.15
t = time to expiry =		1
K = Strike price =		1.25
Rd=Doms. Curr. Rate%=		0.0%	Rf = Forgn. Curr. Rate%=			5.0%
σ = Std dev =		25%
d1 = (ln(S/K)+(r-Rf+σ^2/2)*t)/(σ*t^(1/2)
d1 = (ln(1.15/1.25)+(0-0.05+0.25^2/2)*1)/(0.25*1^(1/2))
d1 = -0.208526
d2 = d1-σ*t^(1/2)
d2 =-0.208526-0.25*1^(1/2)
d2 = -0.458526
N(-d1) = Cumulative standard normal dist. of -d1
N(-d1) =0.658556
N(-d2) = Cumulative standard normal dist. of -d2
N(-d2) =0.7449
Value of put= 0.7449*1.25*e^(-0*1)-1.15*e^(-0.05*1)*0.658556
Value of put= 0.21