FX Smile in the Heston Model

TL;DR

This paper adapts the Heston stochastic volatility model to the FX market, demonstrating its ability to reproduce FX option smiles through calibration and discussing computational methods for efficient pricing.

Contribution

It extends the Heston model to FX options and analyzes its calibration and computational aspects in this new setting.

Findings

FX smile can be reproduced by calibrating three model parameters

Semi-analytical formulas enable fast option pricing in FX

Monte Carlo simulations validate the model's effectiveness

Abstract

The Heston model stands out from the class of stochastic volatility (SV) models mainly for two reasons. Firstly, the process for the volatility is non-negative and mean-reverting, which is what we observe in the markets. Secondly, there exists a fast and easily implemented semi-analytical solution for European options. In this article we adapt the original work of Heston (1993) to a foreign exchange (FX) setting. We discuss the computational aspects of using the semi-analytical formulas, performing Monte Carlo simulations, checking the Feller condition, and option pricing with FFT. In an empirical study we show that the smile of vanilla options can be reproduced by suitably calibrating three out of five model parameters.