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On the Guyon-Lekeufack Volatility Model

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  • Marcel Nutz
  • Andr'es Riveros Valdevenito

Abstract

Guyon and Lekeufack recently proposed a path-dependent volatility model and documented its excellent performance in fitting market data and capturing stylized facts. The instantaneous volatility is modeled 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 of the weightings 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 & Andr'es Riveros Valdevenito, 2023. "On the Guyon-Lekeufack Volatility Model," Papers 2307.01319, arXiv.org, revised Jul 2024.
    • Handle: RePEc:arx:papers:2307.01319
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    References listed on IDEAS

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    1. 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.
    2. David G. Hobson & L. C. G. Rogers, 1998. "Complete Models with Stochastic Volatility," Mathematical Finance, Wiley Blackwell, vol. 8(1), pages 27-48, January.
    3. Rémy Chicheportiche & Jean-Philippe Bouchaud, 2014. "The fine-structure of volatility feedback I: Multi-scale self-reflexivity," Post-Print hal-00722261, HAL.
    4. Gilles Zumbach, 2010. "Volatility conditional on price trends," Quantitative Finance, Taylor & Francis Journals, vol. 10(4), pages 431-442.
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