As in the Black-Scholes model for stock options and the Black model for certain interest rate options, the value of a European option on an FX rate is typically calculated by assuming that the rate follows a log-normal process.

In 1983 Garman and Kohlhagen extended the Black-Scholes model to cope with the presence of two interest rates (one for each currency). Suppose that r_{d} is the risk-free interest rate to expiry of the domestic currency and r_{f} is the foreign currency risk-free interest rate (where domestic currency is the currency in which we obtain the value of the option; the formula also requires that FX rates - both strike and current spot be quoted in terms of "units of domestic currency per unit of foreign currency"). Then the domestic currency value of a call option into the foreign currency is

The value of a put option has value

where :

*S*_{0}is the current spot rate*K*is the strike price*N*is the cumulative normal distribution function*r*_{d}is domestic risk free simple interest rate*r*_{f}is foreign risk free simple interest rate*T*is the time to maturity (calculated according to the appropriate day count convention)- and σ is the volatility of the FX rate.

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