IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v487y2025ics0096300324005708.html
   My bibliography  Save this article

Estimation of parameters and valuation of options written on multiple assets described by uncertain fractional differential equations

Author

Listed:
  • Xin, Yue
  • Zhang, Yi
  • Noorani, Idin
  • Mehrdoust, Farshid
  • Gao, Jinwu

Abstract

This study suggests the pricing problems of options dependent on multiple assets, spread, basket, and quanto options when the asset dynamics are described by the uncertain fractional differential equation. The solutions of these option prices are analytically provided and the algorithms related to each one of these derivatives are designed. For the first time, we apply the minimum cover method to estimate the parameters of the uncertain fractional differential equations based on the real data related to the stock prices of some markets. Through the uncertain hypothesis test, we demonstrate that the estimated uncertain fractional differential equations can successfully fit the observed data. We then experimentally show that the α-paths obtained by the estimated uncertain fractional differential equations favorably cover the sample data. Finally, some numerical experiments based on the uncertain fractional differential equation estimated by the minimum cover method are accomplished to confirm the achievement of the presented results.

Suggested Citation

  • Xin, Yue & Zhang, Yi & Noorani, Idin & Mehrdoust, Farshid & Gao, Jinwu, 2025. "Estimation of parameters and valuation of options written on multiple assets described by uncertain fractional differential equations," Applied Mathematics and Computation, Elsevier, vol. 487(C).
    • Handle: RePEc:eee:apmaco:v:487:y:2025:i:c:s0096300324005708
    DOI: 10.1016/j.amc.2024.129109
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300324005708
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2024.129109?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Tingqing Ye & Baoding Liu, 2022. "Uncertain hypothesis test with application to uncertain regression analysis," Fuzzy Optimization and Decision Making, Springer, vol. 21(2), pages 157-174, June.
    2. Najafi, Alireza & Taleghani, Rahman, 2022. "Fractional Liu uncertain differential equation and its application to finance," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    3. Lu, Ziqiang & Zhu, Yuanguo, 2019. "Numerical approach for solution to an uncertain fractional differential equation," Applied Mathematics and Computation, Elsevier, vol. 343(C), pages 137-148.
    4. He, Liu & Zhu, Yuanguo, 2024. "Nonparametric estimation for uncertain fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    5. Liu He & Yuanguo Zhu & Ziqiang Lu, 2023. "Parameter estimation for uncertain fractional differential equations," Fuzzy Optimization and Decision Making, Springer, vol. 22(1), pages 103-122, March.
    6. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    7. Noorani, Idin & Mehrdoust, Farshid, 2022. "Parameter estimation of uncertain differential equation by implementing an optimized artificial neural network," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    8. Tang, Han & Yang, Xiangfeng, 2021. "Uncertain chemical reaction equation," Applied Mathematics and Computation, Elsevier, vol. 411(C).
    9. Kai Yao & Baoding Liu, 2020. "Parameter estimation in uncertain differential equations," Fuzzy Optimization and Decision Making, Springer, vol. 19(1), pages 1-12, March.
    10. Farshid Mehrdoust & Idin Noorani & Wei Xu, 2023. "Uncertain energy model for electricity and gas futures with application in spark-spread option price," Fuzzy Optimization and Decision Making, Springer, vol. 22(1), pages 123-148, March.
    11. Jin, Ting & Zhu, Yuanguo, 2020. "First hitting time about solution for an uncertain fractional differential equation and application to an uncertain risk index model," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    12. Ziqiang Lu & Hongyan Yan & Yuanguo Zhu, 2019. "European option pricing model based on uncertain fractional differential equation," Fuzzy Optimization and Decision Making, Springer, vol. 18(2), pages 199-217, June.
    13. Jin, Ting & Sun, Yun & Zhu, Yuanguo, 2020. "Time integral about solution of an uncertain fractional order differential equation and application to zero-coupon bond model," Applied Mathematics and Computation, Elsevier, vol. 372(C).
    14. Yang, Xiangfeng & Liu, Yuhan & Park, Gyei-Kark, 2020. "Parameter estimation of uncertain differential equation with application to financial market," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    15. Shi, Gang & Gao, Jinwu, 2021. "European Option Pricing Problems with Fractional Uncertain Processes," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    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. Liu, Hanjie & Zhu, Yuanguo, 2024. "Carbon option pricing based on uncertain fractional differential equation: A binomial tree approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 225(C), pages 13-28.
    2. Jin, Ting & Yang, Xiangfeng, 2021. "Monotonicity theorem for the uncertain fractional differential equation and application to uncertain financial market," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 203-221.
    3. Liu He & Yuanguo Zhu & Ziqiang Lu, 2023. "Parameter estimation for uncertain fractional differential equations," Fuzzy Optimization and Decision Making, Springer, vol. 22(1), pages 103-122, March.
    4. Jin, Ting & Ding, Hui & Xia, Hongxuan & Bao, Jinfeng, 2021. "Reliability index and Asian barrier option pricing formulas of the uncertain fractional first-hitting time model with Caputo type," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    5. Jian Zhou & Yujiao Jiang & Athanasios A. Pantelous & Weiwen Dai, 2023. "A systematic review of uncertainty theory with the use of scientometrical method," Fuzzy Optimization and Decision Making, Springer, vol. 22(3), pages 463-518, September.
    6. Weiwei Wang & Dan A. Ralescu, 2021. "Option pricing formulas based on uncertain fractional differential equation," Fuzzy Optimization and Decision Making, Springer, vol. 20(4), pages 471-495, December.
    7. He, Liu & Zhu, Yuanguo, 2024. "Nonparametric estimation for uncertain fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    8. Tingqing Ye & Baoding Liu, 2023. "Uncertain hypothesis test for uncertain differential equations," Fuzzy Optimization and Decision Making, Springer, vol. 22(2), pages 195-211, June.
    9. Weiwei Wang & Dan A. Ralescu & Panpan Zhang, 2024. "Valuation of convertible bond based on uncertain fractional differential equation," Fuzzy Optimization and Decision Making, Springer, vol. 23(4), pages 513-538, December.
    10. Najafi, Alireza & Taleghani, Rahman, 2022. "Fractional Liu uncertain differential equation and its application to finance," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    11. Jin, Ting & Zhu, Yuanguo, 2020. "First hitting time about solution for an uncertain fractional differential equation and application to an uncertain risk index model," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    12. Jie, Ke-Wei & Liu, San-Yang & Sun, Xiao-Jun & Xu, Yun-Cheng, 2023. "A dynamic ripple-spreading algorithm for solving mean–variance of shortest path model in uncertain random networks," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    13. Chen, Dan & Liu, Yang, 2023. "Uncertain Gordon-Schaefer model driven by Liu process," Applied Mathematics and Computation, Elsevier, vol. 450(C).
    14. Tang, Han & Yang, Xiangfeng, 2022. "Moment estimation in uncertain differential equations based on the Milstein scheme," Applied Mathematics and Computation, Elsevier, vol. 418(C).
    15. Noorani, Idin & Mehrdoust, Farshid, 2022. "Parameter estimation of uncertain differential equation by implementing an optimized artificial neural network," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    16. Wang, Weiwei & Ralescu, Dan A., 2021. "Valuation of lookback option under uncertain volatility model," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    17. Xie, Jinsheng & Lio, Waichon & Kang, Rui, 2024. "Analysis of simple pendulum with uncertain differential equation," Chaos, Solitons & Fractals, Elsevier, vol. 185(C).
    18. Jia, Lifen & Chen, Wei, 2020. "Knock-in options of an uncertain stock model with floating interest rate," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    19. Sheng, Yuhong & Yao, Kai & Qin, Zhongfeng, 2020. "Continuity and variation analysis of fractional uncertain processes," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    20. Yang Liu & Baoding Liu, 2022. "Residual analysis and parameter estimation of uncertain differential equations," Fuzzy Optimization and Decision Making, Springer, vol. 21(4), pages 513-530, December.

    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:eee:apmaco:v:487:y:2025:i:c:s0096300324005708. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.