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arXiv · 2112.02440

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

Claudio Fontana·Alessandro Gnoatto·Guillaume Szulda
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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.

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Claudio Fontana, Alessandro Gnoatto, Guillaume Szulda. 2021-12-04. CBI-time-changed L\'evy processes for multi-currency modeling. https://doi.org/10.1007/s10479-022-04982-z

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