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

TL;DR

The paper introduces the Compound BSDE method, a fully forward deep-learning approach for solving complex option pricing and optimal stopping problems in finance, demonstrating high accuracy and efficiency.

Contribution

It develops a novel algorithm for compound BSDEs, extending deep BSDE methods to a broader class of financial problems with proven convergence and error estimates.

Findings

Accurate solutions for high-dimensional option pricing.

Efficient computational performance demonstrated.

Effective for optimal stopping problems like Bermudan options.

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.