The Pricing of Call and Put Options on Foreign Exchange

This paper derives exact pricing equations for American and European puts and calls on foreign exchange and discusses hedging strategy. Because every call option on foreign currency is simultaneously a put option on the domestic currency, an equivalence relation exists that allows the immediate derivation of put equations from the corresponding call formulas. The call and put pricing formulas are unlike the Black-Scholes equations for stock options in that there are two relevant interest rates, interest rates are stochastic, and boundary constraints differ. In addition, both American call and put options have values larger than their European counterparts.