Foreign exchange option pricing under the 4/2 stochastic volatility model with CIR interest rates.

Abstract

. Foreign exchange (FX) options are studied in a new stochastic volatility model (the 4/2 stochastic volatility model), which includes, as special instances, the Heston model and the 3/2 model, for the exchange rate in combination with the Cox-Ingersoll-Ross (CIR) dynamics for the domestic and foreign stochastic interest rates. We allow the correlation between the instantaneous volatility and the dynamics of the exchange rate, whereas the interest rates in both domestic and foreign markets are assumed to be independent of the dynamics of the exchange rate. We provide a semi-analytical formula for the price of the European FX call option via Fourier inversion. Through the change of measure technique, we derived explicit expressions for conditional characteristic functions. Our model is computationally tractable, thereby the pricing procedure is accurate and illustrates more efficiency in comparison to the Monte Carlo simulation method. Finally, we perform calibrations on market data, demonstrating that our model fits the implied volatilities well and outperforms the Heston model with CIR interest rates.