A review of tree-based approaches to solving forward–backward stochastic differential equations

Long Teng

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Need to know

A regression-tree-based approach is proposed to solve numerically high-dimensional backward stochastic differential equations (BSDEs).
The approach is reviewed from different perspectives, and error analysis is performed.
Several numerical experiments including high-dimensional problems are provided to demonstrate accuracy and performance.
For the applicability of BSDEs in financial problems, the Heston stochastic volatility model and a high-dimensional nonlinear pricing problem are solved with the presented approach via BSDEs.

Abstract

In this work, we study ways of solving (decoupled) forward–backward stochastic differential equations numerically using regression trees. Based on general theta-discretization for 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 accuracy and performance. To show the applicability of forward–backward stochastic differential equations to financial problems, we apply our tree-based approach to the Heston stochastic volatility model to high-dimensional nonlinear pricing problems.

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