Foreign exchange options under stochastic volatility and stochastic interest rates

In this paper, we present a stochastic volatility model with stochastic interest rates in a Foreign Exchange (FX) setting. The instantaneous volatility follows a mean-reverting Ornstein-Uhlenbeck process and is correlated with the exchange rate. The domestic and foreign interest rates are modeled by mean-reverting Ornstein-Uhlenbeck processes. The main result is an analytic formula for the price of a European call on the exchange rate. It is derived using martingale methods in arbitrage pricing of contingent claims and Fourier inversion techniques.