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

Author

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  • Jian Liang
  • Zhe Xu
  • Peter Li

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.

Suggested Citation

  • Jian Liang & Zhe Xu & Peter Li, 2019. "Deep Learning-Based Least Square Forward-Backward Stochastic Differential Equation Solver for High-Dimensional Derivative Pricing," Papers 1907.10578, arXiv.org, revised Oct 2020.
    • Handle: RePEc:arx:papers:1907.10578
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    References listed on IDEAS

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    1. Masaaki Fujii & Akihiko Takahashi & Masayuki Takahashi, 2017. "Asymptotic Expansion as Prior Knowledge in Deep Learning Method for high dimensional BSDEs," Papers 1710.07030, arXiv.org, revised Mar 2019.
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    3. 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.
    4. Barraquand, Jérôme & Martineau, Didier, 1995. "Numerical Valuation of High Dimensional Multivariate American Securities," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 30(3), pages 383-405, September.
    5. Masaaki Fujii & Akihiko Takahashi & Masayuki Takahashi, 2019. "Asymptotic Expansion as Prior Knowledge in Deep Learning Method for high dimensional BSDEs (Forthcoming in Asia-Pacific Financial Markets)," CARF F-Series CARF-F-456, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    6. Masaaki Fujii & Akihiko Takahashi & Masayuki Takahashi, 2019. "Asymptotic Expansion as Prior Knowledge in Deep Learning Method for High dimensional BSDEs," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 26(3), pages 391-408, September.
    7. Jèôme Barraquand, 1995. "Numerical Valuation of High Dimensional Multivariate European Securities," Management Science, INFORMS, vol. 41(12), pages 1882-1891, December.
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    Cited by:

    1. Jiawei Huo, 2023. "Finite Difference Solution Ansatz approach in Least-Squares Monte Carlo," Papers 2305.09166, arXiv.org, revised Nov 2023.
    2. Yajie Yu & Bernhard Hientzsch & Narayan Ganesan, 2020. "Backward Deep BSDE Methods and Applications to Nonlinear Problems," Papers 2006.07635, arXiv.org.

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