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Valuation of convertible bond based on uncertain fractional differential equation

Author

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  • Weiwei Wang

    (Nanjing Forestry University)

  • Dan A. Ralescu

    (University of Cincinnati)

  • Panpan Zhang

    (Shanghai Jiao Tong University)

Abstract

Convertible bond is a hybrid financial derivative with the properties of debt and equity, which provides the holder with a right to convert bond into the issuer’s stock at a prescribed ratio in the future. This paper analyzes the valuation problems of convertible bond on the basis of uncertain fractional differential equation. Then the prices of convertible bond are obtained by means of expected value criterion and optimistic value criterion, respectively. Besides, numerical examples are given to compare expected value models with optimistic value models. Finally, an empirical study is provided to illustrate that the uncertain fractional stock model is superior to the classical stochastic model.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:fuzodm:v:23:y:2024:i:4:d:10.1007_s10700-024-09431-z
    DOI: 10.1007/s10700-024-09431-z
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    References listed on IDEAS

    as
    1. Batten, Jonathan A. & Khaw, Karren Lee-Hwei & Young, Martin R., 2018. "Pricing convertible bonds," Journal of Banking & Finance, Elsevier, vol. 92(C), pages 216-236.
    2. 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.
    3. Ingersoll, Jonathan Jr., 1977. "A contingent-claims valuation of convertible securities," Journal of Financial Economics, Elsevier, vol. 4(3), pages 289-321, May.
    4. 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.
    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. Xiangfeng Yang & Hua Ke, 2023. "Uncertain interest rate model for Shanghai interbank offered rate and pricing of American swaption," Fuzzy Optimization and Decision Making, Springer, vol. 22(3), pages 447-462, September.
    7. repec:cdl:anderf:qt43n1k4jb is not listed on IDEAS
    8. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," The Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 113-147.
    9. 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.
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    Cited by:

    1. Xiangfeng Yang & Haoxuan Li, 2025. "Uncertain finance: a systematic review of recent advances," Fuzzy Optimization and Decision Making, Springer, vol. 24(3), pages 531-561, September.

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