CBI-time-changed L\'evy processes for multi-currency modeling

TL;DR

This paper introduces a novel stochastic volatility model for multiple currencies using CBI-time-changed Lévy processes, capturing FX market risks and self-exciting volatility dynamics with analytical tractability.

Contribution

It develops a new multi-currency FX model based on CBI-time-changed Lévy processes, incorporating self-exciting volatility and affine process properties for analytical solutions.

Findings

Model captures typical FX risk characteristics.

Achieves good market data fit with simple specifications.

Provides semi-closed pricing formula for currency options.

Abstract

We develop a stochastic volatility framework for modeling multiple currencies based on CBI-time-changed L\'evy processes. The proposed framework captures the typical risk characteristics of FX markets and is coherent with the symmetries of FX rates. Moreover, due to the self-exciting behavior of CBI processes, the volatilities of FX rates exhibit self-exciting dynamics. By relying on the theory of affine processes, we show that our approach is analytically tractable and that the model structure is invariant under a suitable class of risk-neutral measures. A semi-closed pricing formula for currency options is obtained by Fourier methods. We propose two calibration methods, also by relying on deep-learning techniques, and show that a simple specification of the model can achieve a good fit to market data on a currency triangle.