Foreign exchange option
In finance, a foreign exchange option is a derivative financial instrument that gives the right but not the obligation to exchange money denominated in one currency into another currency at a pre-agreed exchange rate on a specified date. See Foreign exchange derivative.
Valuation: the Garman–Kohlhagen model
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.The earliest currency options pricing model was published by Biger and Hull,. The model preceded the Garman and Kolhagen's Model. In 1983 Garman and Kohlhagen extended the Black–Scholes model to cope with the presence of two interest rates. Suppose that is the risk-free interest rate to expiry of the domestic currency and is the foreign currency risk-free interest rate. The results are also in the same units and to be meaningful need to be converted into one of the currencies.
Then the domestic currency value of a call option into the foreign currency is
The value of a put option has value
where :