Question

Calculate the value of an eight-month European put option on a currency with a strike price of 0.50. The current exchange rate is 0.52, the volatility of the exchange rate is 12%, the domestic risk-free interest rate is 4% per annum, and the foreign risk-free interest rate is 8% per annum.

Answer 1

As per Garman Kohlhagen model
Value of put option = N(-d2)*K*e^(-Rd*t)-(S*e^(-Rf*t))*N(-d1)
Where
S = Current price =		0.52
t = time to expiry =		0.666
K = Strike price =		0.5
Rd=Doms. Curr. Rate%=		4.0%	Rf = Forgn. Curr. Rate%=			8.0%
σ = Std dev =		12%
d1 = (ln(S/K)+(r-Rf+σ^2/2)*t)/(σ*t^(1/2)
d1 = (ln(0.52/0.5)+(0.04-0.08+0.12^2/2)*0.666)/(0.12*0.666^(1/2))
d1 = 0.72149
d2 = d1-σ*t^(1/2)
d2 =0.72149-0.12*0.666^(1/2)
d2 = 0.623559
N(-d1) = Cumulative standard normal dist. of -d1
N(-d1) =0.429585
N(-d2) = Cumulative standard normal dist. of -d2
N(-d2) =0.468317
Value of put= 0.468317*0.5*e^(-0.04*0.666)-0.52*e^(-0.08*0.666)*0.429585
Value of put= 0.02