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

Author

Listed:
  • Claudio Fontana

    (University of Padova)

  • Alessandro Gnoatto

    (University of Verona)

  • Guillaume Szulda

    (University of Padova
    Université de Paris Cité)

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.

Suggested Citation

  • Claudio Fontana & Alessandro Gnoatto & Guillaume Szulda, 2024. "CBI-time-changed Lévy processes for multi-currency modeling," Annals of Operations Research, Springer, vol. 336(1), pages 127-152, May.
    • Handle: RePEc:spr:annopr:v:336:y:2024:i:1:d:10.1007_s10479-022-04982-z
    DOI: 10.1007/s10479-022-04982-z
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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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