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Random neural networks for rough volatility

Author

Listed:
  • 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 BSDE, 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.

Suggested Citation

  • Antoine Jacquier & Zan Zuric, 2023. "Random neural networks for rough volatility," Papers 2305.01035, arXiv.org, revised Feb 2026.
    • Handle: RePEc:arx:papers:2305.01035
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    References listed on IDEAS

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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, revised Apr 2025.
    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 Jan 2025.
    3. Bo Yuan & Damiano Brigo & Antoine Jacquier & Nicola Pede, 2024. "Deep learning interpretability for rough volatility," Papers 2411.19317, arXiv.org.
    4. Boris Ter-Avanesov & Gunter A. Meissner, 2024. "Pricing Multi-strike Quanto Call Options on Multiple Assets with Stochastic Volatility, Correlation, and Exchange Rates," Papers 2411.16617, arXiv.org.

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