Pricing of foreign exchange options under the Heston stochastic volatility model and CIR interest rates

摘要

Foreign exchange options are studied in the Heston stochastic volatility model for the exchange rate combined with the Cox et al. dynamics for the domestic and foreign stochastic interest rates. 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. The main result furnishes a semi-analytical formula for the price of the foreign exchange European call option. The FX options pricing formula is derived using the probabilistic approach, which leads to explicit expressions for conditional characteristic functions. Stylized numerical examples show that the dynamics of interest rates are important for the valuation of foreign exchange options. We argue that the model examined in this paper is the only analytically tractable version of the foreign exchange market model that combines the Heston stochastic volatility model for the exchange rate with the CIR dynamics for interest rates.