An Affine Multi-Currency Model with Stochastic Volatility and Stochastic Interest Rates

Abstract

We introduce a tractable multi-currency model with stochastic volatility and correlated stochastic interest rates that takes into account the smile in the FX market and the evolution of yield curves. The pricing of vanilla options on FX rates can be performed efficiently through the FFT methodology thanks to the affinity of the model. A joint calibration exercise of the implied volatility surfaces of a triangle of FX rates shows the flexibility of our framework in dealing with the typical symmetries that characterize the FX market. Our framework is also able to describe many non trivial links between FX rates and interest rates: a second calibration exercise highlights the ability of the model to fit simultaneously FX implied volatilities while being coherent with interest rate products.

Keywords: FX options, Hybrid models, longdated FX, Wishart process, Affine process, FFT

JEL Classification: G130, G120, G150