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A time-stepping deep gradient flow method for option pricing in (rough) diffusion models

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  • Antonis Papapantoleon
  • Jasper Rou

Abstract

We develop a novel deep learning approach for pricing European options in diffusion models, that can efficiently handle high-dimensional problems resulting from Markovian approximations of rough volatility models. The option pricing partial differential equation is reformulated as an energy minimization problem, which is approximated in a time-stepping fashion by deep artificial neural networks. The proposed scheme respects the asymptotic behavior of option prices for large levels of moneyness, and adheres to a priori known bounds for option prices. The accuracy and efficiency of the proposed method is assessed in a series of numerical examples, with particular focus in the lifted Heston model.

Suggested Citation

  • Antonis Papapantoleon & Jasper Rou, 2025. "A time-stepping deep gradient flow method for option pricing in (rough) diffusion models," Quantitative Finance, Taylor & Francis Journals, vol. 25(12), pages 2009-2020, December.
    • Handle: RePEc:taf:quantf:v:25:y:2025:i:12:p:2009-2020
    DOI: 10.1080/14697688.2025.2572318
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