Pricing Vanilla European FX Options

Vanilla European FX Options can be valued using the Garman-Kohlhagen model. The formula is identical to the orginal variation of Black-Scholes devised for a dividend paying stock except that the dividend is replaced by the continuously-compounded risk-free rate of the asset (the currenty being bought or sold). If the FX world becomes confusing, it helps to think of one of the currencies as an asset, paying a return, which is being bought using the domestic currency.
Let us look at the Garman-Kohlhagen formula for valuing a call and put: