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

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.

@article{papapantoleon2025_2403.00746,
  title={ A time-stepping deep gradient flow method for option pricing in (rough) diffusion models },
  author={ Antonis Papapantoleon and Jasper Rou },
  journal={arXiv preprint arXiv:2403.00746},
  year={ 2025 }
}