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

2026/01/26 by Zhipeng Huang, Cornelis W. Oosterlee · 1 voice
Economics, Econometrics and Finance · Mathematics · #math.NA #q-fin.CP #q-fin.PR

paper · pdf · doi:10.48550/arxiv.2601.18634

arxiv published 2026/01/26 · arxiv updated 2026/01/30

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.

Citations

• A deep BSDE approach for the simultaneous pricing and delta-gamma hedging of large portfolios consisting of high-dimensional multi-asset Bermudan options
• Generalized convergence of the deep BSDE method: a step towards fully-coupled FBSDEs and applications in stochastic control
• A deep solver for BSDEs with jumps
• Convergence of a robust deep FBSDE method for stochastic control
• Convergence of a Robust Deep FBSDE Method for Stochastic Control
• A posteriori error estimates for fully coupled McKean-Vlasov forward-backward SDEs
• Solving stochastic optimal control problem via stochastic maximum principle with deep learning method
• Deep backward schemes for high-dimensional nonlinear PDEs
• Deep Learning-Based BSDE Solver for Libor Market Model with Application\n to Bermudan Swaption Pricing and Hedging
• Discrete-time approximation of multidimensional BSDEs with oblique reflections
• Time discretization and Markovian iteration for coupled FBSDEs
• A forward scheme for backward SDEs
• Numerical simulation of BSDEs using empirical regression methods: theory and practice
• A regression-based Monte Carlo method to solve backward stochastic differential equations
• Discrete-time approximation and Monte-Carlo simulation of backward stochastic differential equations

Discussions

• Zhipeng Huang, Cornelis W. Oosterlee: The Compounded BSDE method: A fully-forward method for option pricing and optimal stopping problems in finance https://arxiv.org/abs/2601.18634 https://arxiv.org/ [bsky, 0 points, 0 comments]

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