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Deep Curve-dependent PDEs for affine rough volatility

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  • Antoine Jacquier
  • Mugad Oumgari

Abstract

We introduce a new deep-learning based algorithm to evaluate options in affine rough stochastic volatility models. Viewing the pricing function as the solution to a curve-dependent PDE (CPDE), depending on forward curves rather than the whole path of the process, for which we develop a numerical scheme based on deep learning techniques. Numerical simulations suggest that the latter is a promising alternative to classical Monte Carlo simulations.

Suggested Citation

  • Antoine Jacquier & Mugad Oumgari, 2019. "Deep Curve-dependent PDEs for affine rough volatility," Papers 1906.02551, arXiv.org, revised Jan 2023.
    • Handle: RePEc:arx:papers:1906.02551
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    File URL: http://arxiv.org/pdf/1906.02551
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    Cited by:

    1. Marc Sabate-Vidales & David v{S}iv{s}ka & Lukasz Szpruch, 2020. "Solving path dependent PDEs with LSTM networks and path signatures," Papers 2011.10630, arXiv.org.
    2. Alexandre Pannier & Cristopher Salvi, 2024. "A path-dependent PDE solver based on signature kernels," Papers 2403.11738, arXiv.org, revised Oct 2024.
    3. Christian Bayer & Jinniao Qiu & Yao Yao, 2020. "Pricing Options Under Rough Volatility with Backward SPDEs," Papers 2008.01241, arXiv.org.
    4. Ofelia Bonesini & Antoine Jacquier & Alexandre Pannier, 2023. "Rough volatility, path-dependent PDEs and weak rates of convergence," Papers 2304.03042, arXiv.org.
    5. Antonis Papapantoleon & Jasper Rou, 2024. "A time-stepping deep gradient flow method for option pricing in (rough) diffusion models," Papers 2403.00746, arXiv.org.
    6. Alexandre Pannier, 2023. "Path-dependent PDEs for volatility derivatives," Papers 2311.08289, arXiv.org, revised Jan 2024.
    7. Antoine Jacquier & Mugad Oumgari, 2023. "Interest rate convexity in a Gaussian framework," Papers 2307.14218, arXiv.org, revised Mar 2024.
    8. Antoine Jacquier & Zan Zuric, 2023. "Random neural networks for rough volatility," Papers 2305.01035, arXiv.org.
    9. 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 Dec 2024.

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