An analytic multi-currency model with stochastic volatility and stochastic interest rates

TL;DR

This paper presents a tractable multi-currency model incorporating stochastic volatility and interest rates, effectively capturing FX market smiles and yield curve dynamics, enabling efficient option pricing and consistent calibration across FX and interest rate markets.

Contribution

It introduces a novel multi-currency model that jointly models stochastic volatility and interest rates, allowing for efficient FFT-based pricing and simultaneous calibration to FX and interest rate data.

Findings

Model accurately fits FX implied volatilities.

Efficient FFT-based pricing methodology.

Coherent calibration with interest rate products.

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 effciently through the FFT methodology thanks to the affinity of the model 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 fit simultaneously FX implied volatilities while being coherent with interest rate products.