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Pricing American options under rough volatility using deep-signatures and signature-kernels

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  • Christian Bayer
  • Luca Pelizzari
  • Jia-Jie Zhu

Abstract

We extend the signature-based primal and dual solutions to the optimal stopping problem recently introduced in [Bayer et al.: Primal and dual optimal stopping with signatures, to appear in Finance & Stochastics 2025], by integrating deep-signature and signature-kernel learning methodologies. These approaches are designed for non-Markovian frameworks, in particular enabling the pricing of American options under rough volatility. We demonstrate and compare the performance within the popular rough Heston and rough Bergomi models.

Suggested Citation

  • 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.
    • Handle: RePEc:arx:papers:2501.06758
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    References listed on IDEAS

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    1. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," The Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 113-147.
    2. Christian Bayer & Luca Pelizzari & John Schoenmakers, 2023. "Primal and dual optimal stopping with signatures," Papers 2312.03444, arXiv.org, revised Feb 2025.
    3. Lapeyre Bernard & Lelong Jérôme, 2021. "Neural network regression for Bermudan option pricing," Monte Carlo Methods and Applications, De Gruyter, vol. 27(3), pages 227-247, September.
    4. Ryan McCrickerd & Mikko S. Pakkanen, 2018. "Turbocharging Monte Carlo pricing for the rough Bergomi model," Quantitative Finance, Taylor & Francis Journals, vol. 18(11), pages 1877-1886, November.
    5. 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.
    6. Omar El Euch & Mathieu Rosenbaum, 2019. "The characteristic function of rough Heston models," Mathematical Finance, Wiley Blackwell, vol. 29(1), pages 3-38, January.
    7. Christian Bayer & Peter Friz & Jim Gatheral, 2016. "Pricing under rough volatility," Quantitative Finance, Taylor & Francis Journals, vol. 16(6), pages 887-904, June.
    8. L. C. G. Rogers, 2002. "Monte Carlo valuation of American options," Mathematical Finance, Wiley Blackwell, vol. 12(3), pages 271-286, July.
    9. Ryan McCrickerd & Mikko S. Pakkanen, 2017. "Turbocharging Monte Carlo pricing for the rough Bergomi model," Papers 1708.02563, arXiv.org, revised Mar 2018.
    10. Vijay V. Desai & Vivek F. Farias & Ciamac C. Moallemi, 2012. "Pathwise Optimization for Optimal Stopping Problems," Management Science, INFORMS, vol. 58(12), pages 2292-2308, December.
    11. repec:cdl:anderf:qt43n1k4jb is not listed on IDEAS
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    Cited by:

    1. Eduardo Abi Jaber & Louis-Amand Gérard, 2025. "Hedging with memory: shallow and deep learning with signatures," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-05197836, HAL.

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