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

Claudio Fontana, Alessandro Gnoatto and Guillaume Szulda

Papers from arXiv.org

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.

Date: 2021-12, Revised 2022-07
New Economics Papers: this item is included in nep-rmg
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Published in Annals of Operations Research, 336: 127-152, 2024

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