Deep-Learning Based Numerical BSDE Method for Barrier Options

11 Pages Posted: 22 Apr 2019

See all articles by Bing Yu

Bing Yu

Wells Fargo Bank - Corporate Model Risk Management

Xiaojing Xing

Wells Fargo Bank - Corporate Model Risk Management

Agus Sudjianto

Corporate Model Risk, Wells Fargo Bank

Date Written: January 18, 2019

Abstract

As is known, an option price is a solution to a certain partial differential equation (PDE) with terminal conditions (payoff functions). There is a close association between the solution of PDE and the solution of a backward stochastic differential equation (BSDE). We can either solve the PDE to obtain option prices or solve its associated BSDE. Recently a deep learning technique has been applied to solve option prices using the BSDE approach. In this approach, deep learning is used to learn some deterministic functions, which are used in solving the BSDE with terminal conditions. In this paper, we extend the deep-learning technique to solve a PDE with both terminal and boundary conditions. In particular, we will employ the technique to solve barrier options using Brownian motion bridges.

Keywords: Barrier Options, Machine Learning, AI, Deep Learning, BSDE

JEL Classification: G12, G13

Suggested Citation

Yu, Bing and Xing, Xiaojing and Sudjianto, Agus, Deep-Learning Based Numerical BSDE Method for Barrier Options (January 18, 2019). Available at SSRN: https://ssrn.com/abstract=3366314 or http://dx.doi.org/10.2139/ssrn.3366314

Bing Yu (Contact Author)

Wells Fargo Bank - Corporate Model Risk Management ( email )

301 South Tryon Street
Wells Faro Three 10th Floor
Charlotte, NC 28288
United States

Xiaojing Xing

Wells Fargo Bank - Corporate Model Risk Management ( email )

301 South Tryon Street
Wells Faro Three 10th Floor
Charlotte, NC 28288
United States

Agus Sudjianto

Corporate Model Risk, Wells Fargo Bank ( email )

301 South Tryon Street
Wells Faro Three 10th Floor
Charlotte, NC 28288
United States
704-715-9052 (Phone)

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