Black-Scholes Extensions: Garman-Kohlhagen and Black Models

European-style currency options can be priced using the Garman-Kohlhagen formula which is a variant on the Black-Scholes option pricing formula. The original Black-Scholes formula has also been extended to price bond options and interest rate caps and floors. We describe the derivations of both extensions here, and then give a brief discussion on the use of implied volatilities instead of prices for communication between option traders.