Pricing currency options in the Heston/CIR double exponential jump-diffusion model

Abstract

We examine currency options in the double exponential jump-diffusion version of the Heston stochastic volatility model for the exchange rate. We assume, in addition, that the domestic and foreign stochastic interest rates are governed by the CIR dynamics. The instantaneous volatility is correlated with the dynamics of the exchange rate return, whereas the domestic and foreign short-term rates are assumed to be independent of the dynamics of the exchange rate and its volatility. The main result furnishes a semi-analytical formula for the price of the European currency call option in the hybrid foreign exchange/interest rates model.