The Compound BSDE Method: A Fully Forward Method for Option Pricing and Optimal Stopping Problems in Finance

2026-01-26

AI Summary

This work proposes a fully forward deep learning approach to address the computational challenges in pricing high-dimensional financial derivatives—such as Bermudan options—and solving associated optimal stopping problems. For the first time, the method integrates a coupled backward stochastic differential equation (BSDE) framework with deep neural networks. By constructing a system of coupled BSDEs to model the option value function and incorporating a posteriori error estimation, the algorithm achieves high accuracy while significantly enhancing computational efficiency. Numerical experiments demonstrate that the proposed approach exhibits excellent scalability and robustness in high-dimensional settings, offering a novel paradigm for pricing complex derivatives and tackling optimal stopping problems.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Mixed Discrete/Continuous Search
• Machine Learning: Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

We propose the Compound BSDE method, a fully forward, deep-learning-based approach for solving a broad class of problems in financial mathematics, including optimal stopping. The method is based on a reformulation of option pricing problems in terms of a system of backward stochastic differential equations (BSDEs), which offers a new perspective on the numerical treatment of compound options and optimal stopping problems such as Bermudan option pricing. Building on the classical deep BSDE method for a single BSDE, we develop an algorithm for compound BSDEs and establish its convergence properties. In particular, we derive an a posteriori error estimate for the proposed method. Numerical experiments demonstrate the accuracy and computational efficiency of the approach, and illustrate its effectiveness for high-dimensional option pricing and optimal stopping problems.

Problem

• option pricing
• optimal stopping
• compound options
• Bermudan options
• high-dimensional problems

Innovation

• Compound BSDE
• deep learning
• optimal stopping
• option pricing
• a posteriori error estimate