IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v13y2025i4p617-d1590624.html
   My bibliography  Save this article

Deep Learning Artificial Neural Network for Pricing Multi-Asset European Options

Author

Listed:
  • Zhiqiang Zhou

    (School of Economics and Management, Xiangnan University, Chenzhou 423000, China)

  • Hongying Wu

    (School of Mathematics and Information Science, Xiangnan University, Chenzhou 423000, China)

  • Yuezhang Li

    (School of Economics and Management, Xiangnan University, Chenzhou 423000, China)

  • Caijuan Kang

    (School of Economics and Management, Xiangnan University, Chenzhou 423000, China)

  • You Wu

    (School of Economics and Management, Xiangnan University, Chenzhou 423000, China)

Abstract

This paper studies a p -layers deep learning artificial neural network (DLANN) for European multi-asset options. Firstly, a p -layers DLANN is constructed with undetermined weights and bias. Secondly, according to the terminal values of the partial differential equation (PDE) and the points that satisfy the PDE of multi-asset options, some discrete data are fed into the p -layers DLANN. Thirdly, using the least square error as the objective function, the weights and bias of the DLANN are trained well. In order to optimize the objective function, the partial derivatives for the weights and bias of DLANN are carefully derived. Moreover, to improve the computational efficiency, a time-segment DLANN is proposed. Numerical examples are presented to confirm the accuracy, efficiency, and stability of the proposed p -layers DLANN. Computational examples show that the DLANN’s relative error is less than 0.5 % for different numbers of assets d = 1 , 2 , 3 , 4 . In the future, the p -layers DLANN can be extended into American options, Asian options, Lookback options, and so on.

Suggested Citation

  • Zhiqiang Zhou & Hongying Wu & Yuezhang Li & Caijuan Kang & You Wu, 2025. "Deep Learning Artificial Neural Network for Pricing Multi-Asset European Options," Mathematics, MDPI, vol. 13(4), pages 1-26, February.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:4:p:617-:d:1590624
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/13/4/617/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/13/4/617/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Lina Song & Weiguo Wang, 2013. "Solution of the Fractional Black-Scholes Option Pricing Model by Finite Difference Method," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-10, June.
    2. Yuanyang Teng & Yicun Li & Xiaobo Wu & Ya Jia, 2022. "Option Volatility Investment Strategy: The Combination of Neural Network and Classical Volatility Prediction Model," Discrete Dynamics in Nature and Society, Hindawi, vol. 2022, pages 1-39, April.
    3. Carl Chiarella & Boda Kang & Gunter H Meyer, 2014. "The Numerical Solution of the American Option Pricing Problem:Finite Difference and Transform Approaches," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 8736, September.
    4. 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.
    5. Lorenc Kapllani & Long Teng, 2024. "A forward differential deep learning-based algorithm for solving high-dimensional nonlinear backward stochastic differential equations," Papers 2408.05620, arXiv.org.
    6. Zhiqiang Zhou & Wei Xu & Alexey Rubtsov, 2024. "Joint calibration of S&P 500 and VIX options under local stochastic volatility models," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 29(1), pages 273-310, January.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Zhiqiang Zhou & Hongying Wu & Yuezhang Li & Caijuan Kang & You Wu, 2024. "Three-Layer Artificial Neural Network for Pricing Multi-Asset European Option," Mathematics, MDPI, vol. 12(17), pages 1-22, September.
    2. E. Alòs & F. Antonelli & A. Ramponi & S. Scarlatti, 2021. "Cva And Vulnerable Options In Stochastic Volatility Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 24(02), pages 1-34, March.
    3. Panumart Sawangtong & Kamonchat Trachoo & Wannika Sawangtong & Benchawan Wiwattanapataphee, 2018. "The Analytical Solution for the Black-Scholes Equation with Two Assets in the Liouville-Caputo Fractional Derivative Sense," Mathematics, MDPI, vol. 6(8), pages 1-14, July.
    4. Khudair, Ayad R. & Haddad, S.A.M. & khalaf, Sanaa L., 2017. "Restricted fractional differential transform for solving irrational order fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 101(C), pages 81-85.
    5. Lorenc Kapllani & Long Teng, 2024. "A forward differential deep learning-based algorithm for solving high-dimensional nonlinear backward stochastic differential equations," Papers 2408.05620, arXiv.org.
    6. Ludmila Kirianova, 2020. "Modeling of Strength Characteristics of Polymer Concrete Via the Wave Equation with a Fractional Derivative," Mathematics, MDPI, vol. 8(10), pages 1-10, October.
    7. Ketelbuters, John-John & Hainaut, Donatien, 2022. "CDS pricing with fractional Hawkes processes," European Journal of Operational Research, Elsevier, vol. 297(3), pages 1139-1150.
    8. Batra, Luckshay & Taneja, H.C., 2021. "Approximate-Analytical solution to the information measure’s based quanto option pricing model," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    9. Jean-Philippe Aguilar & Jan Korbel & Yuri Luchko, 2019. "Applications of the Fractional Diffusion Equation to Option Pricing and Risk Calculations," Mathematics, MDPI, vol. 7(9), pages 1-23, September.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:13:y:2025:i:4:p:617-:d:1590624. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.