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

• URL: http://arxiv.org/abs/2311.07231v1
• Date: Mon, 13 Nov 2023 10:52:44 GMT
• Title: Error Analysis of Option Pricing via Deep PDE Solvers: Empirical Study
• Abstract summary: We offer actionable insights into the utility of Deep PDE solvers for option pricing implementation. Our investigation identified three primary sources of errors in Deep PDE solvers. Our results indicate that the Deep BSDE method is superior in performance and exhibits robustness against variations in option specifications.
• Score: 2.8303660601968152
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

Related papers

• PDEInvBench: A Comprehensive Dataset and Design Space Exploration of Neural Networks for PDE Inverse Problems [11.742898472476796]
  Intemporal problems in partial differential equations (PDEs) involve estimating the physical parameters of a observed system from solution fields.<n>Nerve networks are well-suited for PDE parameter estimation due to their capability to model function-to-function space transformations.<n>PDEInvBench is a comprehensive benchmark dataset consisting of numerical simulations for both time-dependent and time-independent PDEs.
  arXiv  Detail & Related papers  (2026-05-25T02:13:33Z)
• Towards Fast Option Pricing PDE Solvers Powered by PIELM [0.0]
  Physics-Informed Neural Networks (PINNs) have emerged as a promising approach for solving the forward and inverse problems of partial differential equations (PDEs) using deep learning.<n>This paper introduces Physics-Informed Extreme Learning Machines (PIELMs) as fast alternative to PINNs for solving both forward and inverse problems in financial PDEs.
  arXiv  Detail & Related papers  (2025-10-05T18:50:49Z)
• CodePDE: An Inference Framework for LLM-driven PDE Solver Generation [57.15474515982337]
  Partial differential equations (PDEs) are fundamental to modeling physical systems.<n>Traditional numerical solvers rely on expert knowledge to implement and are computationally expensive.<n>We introduce CodePDE, the first inference framework for generating PDE solvers using large language models.
  arXiv  Detail & Related papers  (2025-05-13T17:58:08Z)
• Error Analysis of Deep PDE Solvers for Option Pricing [0.0]
  Deep learning-based PDE solvers have recently emerged as quick solutions to this problem.<n>Our aim is to offer actionable insights into the utility of deep PDE solvers for practical option pricing implementation.
  arXiv  Detail & Related papers  (2025-05-08T10:45:59Z)
• Paving the way for scientific foundation models: enhancing generalization and robustness in PDEs with constraint-aware pre-training [49.8035317670223]
  A scientific foundation model (SciFM) is emerging as a promising tool for learning transferable representations across diverse domains. We propose incorporating PDE residuals into pre-training either as the sole learning signal or in combination with data loss to compensate for limited or infeasible training data. Our results show that pre-training with PDE constraints significantly enhances generalization, outperforming models trained solely on solution data.
  arXiv  Detail & Related papers  (2025-03-24T19:12:39Z)
• Learning a Neural Solver for Parametric PDE to Enhance Physics-Informed Methods [14.791541465418263]
  We propose learning a solver, i.e., solving partial differential equations (PDEs) using a physics-informed iterative algorithm trained on data. Our method learns to condition a gradient descent algorithm that automatically adapts to each PDE instance. We demonstrate the effectiveness of our method through empirical experiments on multiple datasets.
  arXiv  Detail & Related papers  (2024-10-09T12:28:32Z)
• Unisolver: PDE-Conditional Transformers Are Universal PDE Solvers [55.0876373185983]
  We present the Universal PDE solver (Unisolver) capable of solving a wide scope of PDEs. Our key finding is that a PDE solution is fundamentally under the control of a series of PDE components. Unisolver achieves consistent state-of-the-art results on three challenging large-scale benchmarks.
  arXiv  Detail & Related papers  (2024-05-27T15:34:35Z)
• Deep Equilibrium Based Neural Operators for Steady-State PDEs [100.88355782126098]
  We study the benefits of weight-tied neural network architectures for steady-state PDEs. We propose FNO-DEQ, a deep equilibrium variant of the FNO architecture that directly solves for the solution of a steady-state PDE.
  arXiv  Detail & Related papers  (2023-11-30T22:34:57Z)
• Weak-PDE-LEARN: A Weak Form Based Approach to Discovering PDEs From Noisy, Limited Data [0.0]
  We introduce Weak-PDE-LEARN, a discovery algorithm that can identify non-linear PDEs from noisy, limited measurements of their solutions. We demonstrate the efficacy of Weak-PDE-LEARN by learning several benchmark PDEs.
  arXiv  Detail & Related papers  (2023-09-09T06:45:15Z)
• Deep Operator Learning Lessens the Curse of Dimensionality for PDEs [11.181533339111853]
  This paper provides an estimate for the generalization error of learning Lipschitz operators over Banach spaces using DNNs with applications to various PDE solution operators. Under mild assumptions on data distributions or operator structures, our analysis shows that deep operator learning can have a relaxed dependence on the discretization resolution of PDEs.
  arXiv  Detail & Related papers  (2023-01-28T15:35:52Z)
• Learning differentiable solvers for systems with hard constraints [48.54197776363251]
  We introduce a practical method to enforce partial differential equation (PDE) constraints for functions defined by neural networks (NNs) We develop a differentiable PDE-constrained layer that can be incorporated into any NN architecture. Our results show that incorporating hard constraints directly into the NN architecture achieves much lower test error when compared to training on an unconstrained objective.
  arXiv  Detail & Related papers  (2022-07-18T15:11:43Z)
• Lie Point Symmetry Data Augmentation for Neural PDE Solvers [69.72427135610106]
  We present a method, which can partially alleviate this problem, by improving neural PDE solver sample complexity. In the context of PDEs, it turns out that we are able to quantitatively derive an exhaustive list of data transformations. We show how it can easily be deployed to improve neural PDE solver sample complexity by an order of magnitude.
  arXiv  Detail & Related papers  (2022-02-15T18:43:17Z)
• Physics-Informed Neural Operator for Learning Partial Differential Equations [55.406540167010014]
  PINO is the first hybrid approach incorporating data and PDE constraints at different resolutions to learn the operator. The resulting PINO model can accurately approximate the ground-truth solution operator for many popular PDE families.
  arXiv  Detail & Related papers  (2021-11-06T03:41:34Z)
• Learning MDPs from Features: Predict-Then-Optimize for Sequential Decision Problems by Reinforcement Learning [52.74071439183113]
  We study the predict-then-optimize framework in the context of sequential decision problems (formulated as MDPs) solved via reinforcement learning. Two significant computational challenges arise in applying decision-focused learning to MDPs.
  arXiv  Detail & Related papers  (2021-06-06T23:53:31Z)
• Solver-in-the-Loop: Learning from Differentiable Physics to Interact with Iterative PDE-Solvers [26.444103444634994]
  We show that machine learning can improve the solution accuracy by correcting for effects not captured by the discretized PDE. We find that previously used learning approaches are significantly outperformed by methods that integrate the solver into the training loop. This provides the model with realistic input distributions that take previous corrections into account.
  arXiv  Detail & Related papers  (2020-06-30T18:00:03Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.