A Review of Tree-based Approaches to solve Forward-Backward Stochastic Differential Equations

TL;DR

This paper reviews the use of regression tree methods for numerically solving forward-backward stochastic differential equations, demonstrating their effectiveness in high-dimensional financial models and complex derivatives.

Contribution

It introduces a tree-based numerical approach for FBSDEs using theta-discretization, with applications to high-dimensional financial problems.

Findings

Accurate solutions for high-dimensional FBSDEs demonstrated

Effective in pricing complex financial derivatives

Applicable to models with different interest rates

Abstract

In this work, we study solving (decoupled) forward-backward stochastic differential equations (FBSDEs) numerically using the regression trees. Based on the general theta-discretization for the time-integrands, we show how to efficiently use regression tree-based methods to solve the resulting conditional expectations. Several numerical experiments including high-dimensional problems are provided to demonstrate the accuracy and performance of the tree-based approach. For the applicability of FBSDEs in financial problems, we apply our tree-based approach to the Heston stochastic volatility model, the high-dimensional pricing problems of a Rainbow option and an European financial derivative with different interest rates for borrowing and lending.