CBI-time-changed Lévy processes for multi-currency modeling

Claudio Fontana (), Alessandro Gnoatto and Guillaume Szulda ()
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Claudio Fontana: Department of Mathematics “Tullio Levi Civita”, University of Padova
Guillaume Szulda: Laboratoire de Probabilités, Statistique et Mode ́lisation (LPSM), Paris Diderot University

No 14/2021, Working Papers from University of Verona, Department of Economics

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.

Keywords: FX market; multi-currency market; branching process; self-exciting process; time-change; stochastic volatility; deep calibration; affine process (search for similar items in EconPapers)
JEL-codes: C02 C60 G13 G15 (search for similar items in EconPapers)
Pages: 24
Date: 2021-12
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Working Paper: CBI-time-changed L\'evy processes for multi-currency modeling (2022)
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