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Deep-learning based numerical BSDE method for barrier options

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  • Bing Yu
  • Xiaojing Xing
  • Agus Sudjianto

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.

Suggested Citation

  • Bing Yu & Xiaojing Xing & Agus Sudjianto, 2019. "Deep-learning based numerical BSDE method for barrier options," Papers 1904.05921, arXiv.org.
    • Handle: RePEc:arx:papers:1904.05921
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    File URL: http://arxiv.org/pdf/1904.05921
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    References listed on IDEAS

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    1. Haojie Wang & Han Chen & Agus Sudjianto & Richard Liu & Qi Shen, 2018. "Deep Learning-Based BSDE Solver for Libor Market Model with Application to Bermudan Swaption Pricing and Hedging," Papers 1807.06622, arXiv.org, revised Sep 2018.
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    Cited by:

    1. Jiequn Han & Ruimeng Hu & Jihao Long, 2020. "Convergence of Deep Fictitious Play for Stochastic Differential Games," Papers 2008.05519, arXiv.org, revised Mar 2021.

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