# Error Analysis of Option Pricing via Deep PDE Solvers: Empirical Study

arXiv: https://arxiv.org/abs/2311.07231 · HTML: https://mlsanity.com/paper/2311.07231/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 29 references that are in the map.
- First posted on arXiv 13 Nov 2023.

## Builds on (most cited first, 8 of 8)

- [Solving high-dimensional partial differential equations using deep learning](https://mlsanity.com/paper/1707.02568/) (2017)
- [Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations](https://mlsanity.com/paper/1706.04702/) (2017)
- [Algorithms for Solving High Dimensional PDEs: From Nonlinear Monte Carlo to Machine Learning](https://mlsanity.com/paper/2008.13333/) (2020)
- [An overview on deep learning-based approximation methods for partial differential equations](https://mlsanity.com/paper/2012.12348/) (2020)
- [A proof that artificial neural networks overcome the curse of dimensionality in the numerical approximation of Black-Scholes partial differential equations](https://mlsanity.com/paper/1809.02362/) (2018)
- [Deep splitting method for parabolic PDEs](https://mlsanity.com/paper/1907.03452/) (2019)
- [Neural networks-based algorithms for stochastic control and PDEs in finance](https://mlsanity.com/paper/2101.08068/) (2021)
- [Approximation error analysis of some deep backward schemes for nonlinear PDEs](https://mlsanity.com/paper/2006.01496/) (2020)

## Built on by (most cited first, 2 of 2)

- [Error Analysis of Deep PDE Solvers for Option Pricing](https://mlsanity.com/paper/2505.05121/) (2025)
- [A Schr"odinger Eigenfunction Method for Long-Horizon Stochastic Optimal Control](https://mlsanity.com/paper/2603.23173/) (2026)

## Abstract (arXiv)

Option pricing, a fundamental problem in finance, often requires solving non-linear partial differential equations (PDEs). When dealing with multi-asset options, such as rainbow options, these PDEs become high-dimensional, leading to challenges posed by the curse of dimensionality. While deep learning-based PDE solvers have recently emerged as scalable solutions to this high-dimensional problem, their empirical and quantitative accuracy remains not well-understood, hindering their real-world applicability. In this study, we aimed to offer actionable insights into the utility of Deep PDE solvers for practical option pricing implementation. Through comparative experiments, we assessed the empirical performance of these solvers in high-dimensional contexts. Our investigation identified three primary sources of errors in Deep PDE solvers: (i) errors inherent in the specifications of the target option and underlying assets, (ii) errors originating from the asset model simulation methods, and (iii) errors stemming from the neural network training. Through ablation studies, we evaluated the individual impact of each error source. Our results indicate that the Deep BSDE method (DBSDE) is superior in performance and exhibits robustness against variations in option specifications. In contrast, some other methods are overly sensitive to option specifications, such as time to expiration. We also find that the performance of these methods improves inversely proportional to the square root of batch size and the number of time steps. This observation can aid in estimating computational resources for achieving desired accuracies with Deep PDE solvers.