Hidden Correlations: A Self-Exciting Tale from the FX World

Abstract

The aim of this paper is to investigate the dependence between exchange rates and their volatility from the information synthesised into currency options quotes. To this purpose, we propose an affine stochastic volatility model with self-exciting structure under a timechanged pure jump Lévy framework. In particular, we construct a mechanism inducing dependence effects via systematic jumps. The performance analysis shows that this factor construction marginally improves the pricing of FX options in terms of calibration and fit of the implied volatility surface, indicating that this dependence is of moderate nature. Therefore, we have evidence to claim that there exists a mild correlation between exchange rates and their volatility.

Keywords: Volatility Skew, Time-Changed Lévy Processes, Affine

JEL Classification: C51, D52, G12, G13