Embedding Stochastic Correlation into the Pricing of FX Quanto Options under Stochastic Volatility Models

Abstract

The aim of the paper is to incorporate a stochastic correlation structure when pricing quanto options under the assumption that both the underlying asset and the foreign exchange (FX) rate follow a stochastic volatility model. This is reached not only assuming that the correlation between the underlying asset and its variance process is stochastic (and the same between the exchange rate and its variance process), but also assuming a stochastic correlation between the underlying asset and the exchange rate. Under different stochastic correlation processes specifications, by approximating non-affine terms, we derive a closed-form approximation for the characteristic function of the underlying asset. Numerical experiments and comparison with Monte Carlo simulations are discussed. The analytical tractability of the formulas allows for fast pricing and calibration purposes.