# Error Analysis of Deep PDE Solvers for Option Pricing

arXiv: https://arxiv.org/abs/2505.05121 · HTML: https://mlsanity.com/paper/2505.05121/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 19 references that are in the map.
- First posted on arXiv 8 May 2025.

## Builds on (most cited first, 10 of 10)

- [DGM: A deep learning algorithm for solving partial differential equations](https://mlsanity.com/paper/1708.07469/) (2017)
- [Solving high-dimensional partial differential equations using deep learning](https://mlsanity.com/paper/1707.02568/) (2017)
- [Deep Hedging](https://mlsanity.com/paper/1802.03042/) (2018)
- [Global Convergence of Deep Galerkin and PINNs Methods for Solving Partial Differential Equations](https://mlsanity.com/paper/2305.06000/) (2023)
- [Pricing options and computing implied volatilities using neural networks](https://mlsanity.com/paper/1901.08943/) (2019)
- [An Overview on Machine Learning Methods for Partial Differential Equations: from Physics Informed Neural Networks to Deep Operator Learning](https://mlsanity.com/paper/2408.13222/) (2024)
- [A deep implicit-explicit minimizing movement method for option pricing in jump-diffusion models](https://mlsanity.com/paper/2401.06740/) (2024)
- [Machine learning for option pricing: an empirical investigation of network architectures](https://mlsanity.com/paper/2307.07657/) (2023)
- [A time-stepping deep gradient flow method for option pricing in (rough) diffusion models](https://mlsanity.com/paper/2403.00746/) (2024)
- [Error Analysis of Option Pricing via Deep PDE Solvers: Empirical Study](https://mlsanity.com/paper/2311.07231/) (2023)

## Abstract (arXiv)

Option pricing often requires solving partial differential equations (PDEs). Although deep learning-based PDE solvers have recently emerged as quick solutions to this problem, their empirical and quantitative accuracy remain not well understood, hindering their real-world applicability. In this research, our aim is to offer actionable insights into the utility of deep PDE solvers for practical option pricing implementation. Through comparative experiments in both the Black--Scholes and the Heston model, we assess the empirical performance of two neural network algorithms to solve PDEs: the Deep Galerkin Method and the Time Deep Gradient Flow method (TDGF). We determine their empirical convergence rates and training time as functions of (i) the number of sampling stages, (ii) the number of samples, (iii) the number of layers, and (iv) the number of nodes per layer. For the TDGF, we also consider the order of the discretization scheme and the number of time steps.