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On the Guyon–Lekeufack volatility model

Author

Listed:
  • Marcel Nutz

    (Columbia University)

  • Andrés Riveros Valdevenito

    (Columbia University)

Abstract

Guyon and Lekeufack (Quant. Finance 23:1221–1258, 2023) recently proposed a path-dependent volatility model and documented its excellent performance in fitting market data and capturing stylised facts. The instantaneous volatility is modelled as a linear combination of two processes; one is an integral of weighted past price returns and the other is the square root of an integral of weighted past squared volatility. Each weighting is built using two exponential kernels reflecting long and short memory. Mathematically, the model is a coupled system of four stochastic differential equations. Our main result is the wellposedness of this system: the model has a unique strong (non-explosive) solution for all parameter values. We also study the positivity of the resulting volatility process and the martingale property of the associated exponential price process.

Suggested Citation

  • Marcel Nutz & Andrés Riveros Valdevenito, 2024. "On the Guyon–Lekeufack volatility model," Finance and Stochastics, Springer, vol. 28(4), pages 1203-1223, October.
    • Handle: RePEc:spr:finsto:v:28:y:2024:i:4:d:10.1007_s00780-024-00544-2
    DOI: 10.1007/s00780-024-00544-2
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    References listed on IDEAS

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    1. Julien Guyon & Jordan Lekeufack, 2023. "Volatility is (mostly) path-dependent," Post-Print hal-04373380, HAL.
    2. Gilles Zumbach, 2010. "Volatility conditional on price trends," Quantitative Finance, Taylor & Francis Journals, vol. 10(4), pages 431-442.
    3. Julien Guyon & Jordan Lekeufack, 2023. "Volatility is (mostly) path-dependent," Quantitative Finance, Taylor & Francis Journals, vol. 23(9), pages 1221-1258, September.
    4. Paolo Foschi & Andrea Pascucci, 2008. "Path dependent volatility," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 31(1), pages 13-32, May.
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    Cited by:

    1. Hervé Andrès & Benjamin Jourdain, 2025. "Existence, uniqueness and positivity of solutions to the Guyon-Lekeufack path-dependent volatility model with general kernels," Post-Print hal-04667144, HAL.

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    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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