Deep Learning-Based Least Square Forward-Backward Stochastic Differential Equation Solver for High-Dimensional Derivative Pricing

22 Pages Posted: 11 Jun 2019 Last revised: 24 Jul 2019

See all articles by Jian Liang

Jian Liang

Wells Fargo Bank

Zhe Xu

Wells Fargo Bank

Peter Li

Wells Fargo Bank

Date Written: July 23, 2019

Abstract

We propose a new forward-backward stochastic differential equation solver for high-dimensional derivatives pricing problems by combining deep learning solver with least square regression technique widely used in the least square Monte Carlo method for the valuation of American options. Our numerical experiments demonstrate the efficiency and accuracy of our least square backward deep neural network solver and its capability to provide accurate prices for complex early exercise derivatives such as callable yield notes. Our method can serve as a generic numerical solver for pricing derivatives across various asset groups, in particular, as an efficient means for pricing high-dimensional derivatives with early exercises features.

Keywords: partial differential equation (PDE), forward-backward stochastic differential equation (FBSDE), deep neural network (DNN), least square regression (LSQ), derivative pricing, Bermudan option, callable yield note (CYN), high-dimensional derivative pricing

Suggested Citation

Liang, Jian and Xu, Zhe and Li, Peter, Deep Learning-Based Least Square Forward-Backward Stochastic Differential Equation Solver for High-Dimensional Derivative Pricing (July 23, 2019). Available at SSRN: https://ssrn.com/abstract=3381794 or http://dx.doi.org/10.2139/ssrn.3381794

Jian Liang (Contact Author)

Wells Fargo Bank

United States

Zhe Xu

Wells Fargo Bank

United States

Peter Li

Wells Fargo Bank

United States

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