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

Author

Listed:
  • Claudio Fontana

    (Department of Mathematics “Tullio Levi Civita”, University of Padova)

  • Alessandro Gnoatto

    (Department of Economics (University of Verona))

  • Guillaume Szulda

    (Laboratoire de Probabilités, Statistique et Mode ́lisation (LPSM), Paris Diderot University)

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.

Suggested Citation

  • Claudio Fontana & Alessandro Gnoatto & Guillaume Szulda, 2021. "CBI-time-changed Lévy processes for multi-currency modeling," Working Papers 14/2021, University of Verona, Department of Economics.
    • Handle: RePEc:ver:wpaper:14/2021
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    References listed on IDEAS

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    Cited by:

    1. Fontana, Claudio & Gnoatto, Alessandro & Szulda, Guillaume, 2023. "CBI-time-changed Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 163(C), pages 323-349.

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    More about this item

    Keywords

    FX market; multi-currency market; branching process; self-exciting process; time-change; stochastic volatility; deep calibration; affine process;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G15 - Financial Economics - - General Financial Markets - - - International Financial Markets

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