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

arXiv: https://arxiv.org/abs/2403.00746 · HTML: https://mlsanity.com/paper/2403.00746/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 54 references that are in the map.
- First posted on arXiv 1 Mar 2024.

## Builds on (most cited first, 5 of 5)

- [DGM: A deep learning algorithm for solving partial differential equations](https://mlsanity.com/paper/1708.07469/) (2017)
- [The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems](https://mlsanity.com/paper/1710.00211/) (2017)
- [Solving high-dimensional partial differential equations using deep learning](https://mlsanity.com/paper/1707.02568/) (2017)
- [The Deep Minimizing Movement Scheme](https://mlsanity.com/paper/2109.14851/) (2021)
- [A deep implicit-explicit minimizing movement method for option pricing in jump-diffusion models](https://mlsanity.com/paper/2401.06740/) (2024)

## Built on by (most cited first, 3 of 3)

- [Error Analysis of Deep PDE Solvers for Option Pricing](https://mlsanity.com/paper/2505.05121/) (2025)
- [Time Deep Gradient Flow Method for pricing American options](https://mlsanity.com/paper/2507.17606/) (2025)
- [Convergence of the generalization error for deep gradient flow methods for PDEs](https://mlsanity.com/paper/2512.25017/) (2025)

## Abstract (arXiv)

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.