Question

Find the value of a European foreign currency call if the spot rate is $5.25, the exercise price is $5.40, the domestic interest rate is 6.1 percent, the foreign interest rate is 5.5 percent, the call expires in one month, and the volatility is 0.32. (The interest rates are continuously compounded.)

Please solve with formula, not excel.

Answer 1

The Value of European Call option can be found out by Garman Kohlhagen Model

C=S*e^(-rf*t) *N(d1)-K*e^(-rd*t) * N(d2)

and d1= ( ln(S/K) + (rd-rf + s^2/2) *t ) / (s*t^0.5)

d2 = ( ln(S/K) + (rd-rf - s^2/2) *t ) / (s*t^0.5)

where

S= spot exchange rate = $5.25

K = Exercise price = $5.40

rd= domestic interest rate = 0.061

rf= foreign interest rate =0.055

t= 1 month = 1/12

s =volatility = 0.32

Using the formulas

d1= -0.253358, N(d1)= area under normal distribution till (z= -0.253358) = 0.3999958

d2= -0.3457341 , N(d2) =0.3647713

So, C= 5.25*exp(-0.055*1/12)*0.3999958 - 5.4*exp (-0.061*1/12)*0.3647713

=0.130598

So, the value of the Call option is $0.13 apx