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Option pricing under non-Markovian stochastic volatility models: A deep signature approach

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  • Jingtang Ma
  • Xianglin Wu
  • Wenyuan Li

Abstract

This paper studies the pricing problem in which the underlying asset follows a non-Markovian stochastic volatility model. Classical partial differential equation methods face significant challenges in this context, as the option prices depend not only on the current state, but also on the entire historical path of the process. To overcome these difficulties, we reformulate the asset dynamics as a rough stochastic differential equation and then represent the rough paths via linear or non-linear combinations of time-extended Brownian motion signatures. This representation transforms a rough stochastic differential equation to a classical stochastic differential equation, allowing the application of standard analytical tools. We propose a deep signature approach for both linear and nonlinear representations and rigorously prove the convergence of the algorithm. Numerical examples demonstrate the effectiveness of our approach for both Markovian and non-Markovian volatility models, offering a theoretically grounded and computationally efficient framework for option pricing.

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  • Jingtang Ma & Xianglin Wu & Wenyuan Li, 2025. "Option pricing under non-Markovian stochastic volatility models: A deep signature approach," Papers 2508.15237, arXiv.org.
    • Handle: RePEc:arx:papers:2508.15237
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    References listed on IDEAS

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    1. Goudenège, Ludovic & Molent, Andrea & Zanette, Antonino, 2022. "Moving average options: Machine learning and Gauss-Hermite quadrature for a double non-Markovian problem," European Journal of Operational Research, Elsevier, vol. 303(2), pages 958-974.
    2. Peter Bank & Christian Bayer & Peter K. Friz & Luca Pelizzari, 2025. "Rough PDEs for Local Stochastic Volatility Models," Mathematical Finance, Wiley Blackwell, vol. 35(3), pages 661-681, July.
    3. Peter Bank & Christian Bayer & Peter K. Friz & Luca Pelizzari, 2023. "Rough PDEs for local stochastic volatility models," Papers 2307.09216, arXiv.org, revised Mar 2025.
    4. Omar El Euch & Mathieu Rosenbaum, 2019. "The characteristic function of rough Heston models," Mathematical Finance, Wiley Blackwell, vol. 29(1), pages 3-38, January.
    5. Eduardo Abi Jaber & Louis-Amand G'erard, 2024. "Signature volatility models: pricing and hedging with Fourier," Papers 2402.01820, arXiv.org, revised Jun 2025.
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    7. Erhan Bayraktar & Qi Feng & Zhaoyu Zhang, 2022. "Deep Signature Algorithm for Multi-dimensional Path-Dependent Options," Papers 2211.11691, arXiv.org, revised Jan 2024.
    8. Eduardo Abi Jaber & Louis-Amand Gérard, 2025. "Signature volatility models: pricing and hedging with Fourier," Post-Print hal-04435238, HAL.
    9. Christian Bayer & Luca Pelizzari & Jia-Jie Zhu, 2025. "Pricing American options under rough volatility using deep-signatures and signature-kernels," Papers 2501.06758, arXiv.org, revised Jun 2025.
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