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Random neural networks for rough volatility

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  • Antoine Jacquier
  • Zan Zuric

Abstract

We construct a deep learning-based numerical algorithm to solve path-dependent partial differential equations arising in the context of rough volatility. Our approach is based on interpreting the PDE as a solution to an SPDE, building upon recent insights by Bayer, Qiu and Yao, and on constructing a neural network of reservoir type as originally developed by Gonon, Grigoryeva, Ortega. The reservoir approach allows us to formulate the optimisation problem as a simple least-square regression for which we prove theoretical convergence properties.

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  • Antoine Jacquier & Zan Zuric, 2023. "Random neural networks for rough volatility," Papers 2305.01035, arXiv.org.
    • Handle: RePEc:arx:papers:2305.01035
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    File URL: http://arxiv.org/pdf/2305.01035
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    References listed on IDEAS

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    1. Mikkel Bennedsen & Asger Lunde & Mikko S Pakkanen, 2022. "Decoupling the Short- and Long-Term Behavior of Stochastic Volatility [Multifactor Approximation of Rough Volatility Models]," Journal of Financial Econometrics, Oxford University Press, vol. 20(5), pages 961-1006.
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    Cited by:

    1. Antonis Papapantoleon & Jasper Rou, 2024. "A time-stepping deep gradient flow method for option pricing in (rough) diffusion models," Papers 2403.00746, arXiv.org.
    2. Ariel Neufeld & Philipp Schmocker & Sizhou Wu, 2024. "Full error analysis of the random deep splitting method for nonlinear parabolic PDEs and PIDEs," Papers 2405.05192, arXiv.org, revised Sep 2024.

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