Currency options

European currency options grant the holder the right to buy (call option) or sell (put option) currency at a predetermined exchange rate (strike price or exercise price, X), on a specified date (maturity, T). These financial assets are also called foreign exchange options (or FX options), but to avoid confusion with the term "exchange option", we prefer the "currency option" terminology.

A basic assumption of the original Black-Scholes model (Black and Sholes, 1973, see also Merton, 1973) is that the underlying is a stock that pays no dividend. More generally, the results of the model are held only if the underlying does not grant any kind of yield and does not generate any kind of cost either. However, this assumption might be relaxed easily, and an extended version of the Black-Scholes formula is valid for currency options as well, while all the logic and argumentation of the model is unchanged.

The closed form formula for the price of a European currency...