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A Deep Learning Based Numerical PDE Method for Option Pricing

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Abstract

Proper pricing of options in the financial derivative market is crucial. For many options, it is often impossible to obtain analytical solutions to the Black–Scholes (BS) equation. Hence an accurate and fast numerical method is very beneficial for option pricing. In this paper, we use the Physics-Informed Neural Networks (PINNs) method recently developed by Raissi et al. (J Comput Phys 378:686–707, 2019) to solve the BS equation. Many experiments have been carried out for solving various option pricing models. Compared with traditional numerical methods, the PINNs based method is simple in implementation, but with comparable accuracy and computational speed, which illustrates a promising potential of deep neural networks for solving more complicated BS equations.

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Acknowledgements

Jichun Li would like to thank UNLV for granting his sabbatical leave during Spring 2021 so that he could enjoy his time working on this paper. We also like to thank four anonymous reviewers for their insightful comments that improved this paper.

Funding

Work partially supported by National Natural Science Foundation of China under Grants No. 11961048, NSF of Jiangxi Province with No.20181ACB20001, and National Science Foundation under Grant No. DMS-2011943.

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Authors and Affiliations

  1. Department of Mathematical Sciences, and Institute of Mathematics and Interdisciplinary Sciences, Nanchang University, Nanchang, China

    Xiang Wang

  2. Program in Applied Mathematics and Computer Science, Brown University, Providence, RI, 02912, USA

    Jessica Li

  3. Department of Mathematical Sciences, University of Nevada, Las Vegas, NV, 89154-4020, USA

    Jichun Li

Authors
  1. Xiang Wang
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  2. Jessica Li
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  3. Jichun Li
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Correspondence to Jichun Li.

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Wang, X., Li, J. & Li, J. A Deep Learning Based Numerical PDE Method for Option Pricing. Comput Econ 62, 149–164 (2023). https://doi.org/10.1007/s10614-022-10279-x

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