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

Claudio Fontana (), Alessandro Gnoatto () and Guillaume Szulda ()
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Claudio Fontana: University of Padova
Alessandro Gnoatto: University of Verona
Guillaume Szulda: University of Padova

Annals of Operations Research, 2024, vol. 336, issue 1, No 6, 127-152

Abstract: Abstract We develop a stochastic volatility framework for modeling multiple currencies based on CBI-time-changed Lévy 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; 60G51; 60J85; 91G20; 91G30; 91G60 (search for similar items in EconPapers)
JEL-codes: C02 C60 G13 G15 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10479-022-04982-z

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