The Compounded BSDE method: A fully-forward method for option pricing and optimal stopping problems in finance

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 \emph{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.