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Deep learning-based least squares 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 derivative pricing problems by combining a deep learning solver with a least squares regression technique widely used in the least squares Monte Carlo method for the valuation of American options. Our numerical experiments demonstrate the accuracy of our least squares backward deep neural network solver and its capability to produce accurate prices for complex early exercisable 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 accurate means for pricing high-dimensional derivatives with early exercise features.

Suggested Citation

  • Jian Liang & Zhe Xu & Peter Li, 2021. "Deep learning-based least squares forward-backward stochastic differential equation solver for high-dimensional derivative pricing," Quantitative Finance, Taylor & Francis Journals, vol. 21(8), pages 1309-1323, August.
    • Handle: RePEc:taf:quantf:v:21:y:2021:i:8:p:1309-1323
    DOI: 10.1080/14697688.2021.1881149
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    Cited by:

    1. Bernhard Hientzsch, 2023. "Reinforcement Learning and Deep Stochastic Optimal Control for Final Quadratic Hedging," Papers 2401.08600, arXiv.org.
    2. Riu Naito & Toshihiro Yamada, 2024. "Deep Kusuoka Approximation: High-Order Spatial Approximation for Solving High-Dimensional Kolmogorov Equations and Its Application to Finance," Computational Economics, Springer;Society for Computational Economics, vol. 64(3), pages 1443-1461, September.
    3. Lorenc Kapllani & Long Teng, 2024. "A backward differential deep learning-based algorithm for solving high-dimensional nonlinear backward stochastic differential equations," Papers 2404.08456, arXiv.org.
    4. Ali Fathi & Bernhard Hientzsch, 2023. "A Comparison of Reinforcement Learning and Deep Trajectory Based Stochastic Control Agents for Stepwise Mean-Variance Hedging," Papers 2302.07996, arXiv.org, revised Nov 2023.

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