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European option pricing model based on uncertain fractional differential equation

Author

Listed:
  • Ziqiang Lu

    (Nanjing University of Science and Technology)

  • Hongyan Yan

    (Nanjing Forestry University)

  • Yuanguo Zhu

    (Nanjing University of Science and Technology)

Abstract

In this paper, we investigate a new version of stock model under uncertain circumstances for uncertain stock markets. Firstly, solutions to some uncertain fractional differential equations are presented by employing the Mittag-Leffler function. Then, a new uncertain stock model with mean-reverting process is formulated on the basis of uncertain fractional differential equations. Finally, European option pricing formulas based on the proposed model are investigated as well as some numerical examples.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:fuzodm:v:18:y:2019:i:2:d:10.1007_s10700-018-9293-4
    DOI: 10.1007/s10700-018-9293-4
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    References listed on IDEAS

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    1. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    2. Yiyao Sun & Taoyong Su, 2017. "Mean-reverting stock model with floating interest rate in uncertain environment," Fuzzy Optimization and Decision Making, Springer, vol. 16(2), pages 235-255, June.
    3. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    4. Xiaoyu Ji & Hua Ke, 2017. "No-arbitrage theorem for multi-factor uncertain stock model with floating interest rate," Fuzzy Optimization and Decision Making, Springer, vol. 16(2), pages 221-234, June.
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    Citations

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    Cited by:

    1. 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).
    2. Wang, Jian & Zhu, Yuanguo & Gu, Yajing & Lu, Ziqiang, 2021. "Solutions of linear uncertain fractional order neutral differential equations," Applied Mathematics and Computation, Elsevier, vol. 407(C).
    3. Caiwen Gao & Zhiqiang Zhang & Baoliang Liu, 2022. "Uncertain Population Model with Jumps," Mathematics, MDPI, vol. 10(13), pages 1-12, June.
    4. Qinyun Lu & Yuanguo Zhu, 2020. "Finite-time stability of uncertain fractional difference equations," Fuzzy Optimization and Decision Making, Springer, vol. 19(2), pages 239-249, June.
    5. Liu, Yiyu & Zhu, Yuanguo & Lu, Ziqiang, 2021. "On Caputo-Hadamard uncertain fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    6. Yan, Hongyan & Jin, Ting & Sun, Yun, 2020. "Uncertain bang–bang control problem for multi-stage switched systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 551(C).
    7. 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).
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. Shu, Yadong & Li, Bo, 2022. "Existence and uniqueness of solutions to uncertain fractional switched systems with an uncertain stock model," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    13. 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.
    14. 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).
    15. Kai Yao & Zhongfeng Qin, 2021. "Barrier option pricing formulas of an uncertain stock model," Fuzzy Optimization and Decision Making, Springer, vol. 20(1), pages 81-100, March.

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