Question

The Black-Scholes-Merton model can be used with currency options by replacing the dividend yield with the foreign interest rate.​

True or False

Answer 1

The statement is TRUE.

It is true that the Black Scholes Merton Model can be used with currency options by replacing the dividend yield with the foreign interest rate .

A foreign currency is analogus to a stock paying a dividend yield in terms of risk free foreign interest rate. So we can replace the dividend yield q in the equation with risk free interest in foreign currency rf .

The valuation formula for European Currency options where rf=risk free interest in foreign currency are ;

c= S0e^-rfT*N(d1) -Ke^-rT*N(d2)
p= Ke^-rT*N(-d2) -S0e^-rfT*N(-d1)

where
d1= [ln(S0/K) +(r -rf+sigma^2/2)*T]/[Sigma*Sq Rt of T]
d2= [ln(S0/K) +(r-rf-sigma^2/2)*T]/[Sigma*Sq Rt of T]
=d1 - Sigma*Sq Rt of T