IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v534y2019ics0378437119313573.html
   My bibliography  Save this article

Extreme values for solution to uncertain fractional differential equation and application to American option pricing model

Author

Listed:
  • Jin, Ting
  • Sun, Yun
  • Zhu, Yuanguo

Abstract

Uncertain fractional differential equation plays an important role of describing uncertain dynamic process. This paper focuses on extreme values (including supremum and infimum) for solution to an uncertain fractional differential equation for the Caputo type. Theorems for the inverse uncertain distributions of the extreme values are given based on the definition of α-path. And then, numerical algorithms for them are designed, numerical examples are shown for validating the availability about algorithms. The absolute errors between the numerical and analytical results are also presented to demonstrate the accuracy of the algorithms. Finally, as an application of the extreme values, an uncertain stock model is proposed on the basis of uncertain fractional differential equation of the Caputo type. The American option pricing formulas of such stock model are studied by using the proposed extreme theorems. Besides, numerical calculations are also illustrated with respect to different parameters p.

Suggested Citation

  • Jin, Ting & Sun, Yun & Zhu, Yuanguo, 2019. "Extreme values for solution to uncertain fractional differential equation and application to American option pricing model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).
    • Handle: RePEc:eee:phsmap:v:534:y:2019:i:c:s0378437119313573
    DOI: 10.1016/j.physa.2019.122357
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437119313573
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2019.122357?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. 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.
    2. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. 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).
    3. 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).
    4. 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.
    5. 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.

    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. 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. 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).
    3. William R. Morgan, 2023. "Finance Must Be Defended: Cybernetics, Neoliberalism and Environmental, Social, and Governance (ESG)," Sustainability, MDPI, vol. 15(4), pages 1-21, February.
    4. Filipe Fontanela & Antoine Jacquier & Mugad Oumgari, 2019. "A Quantum algorithm for linear PDEs arising in Finance," Papers 1912.02753, arXiv.org, revised Feb 2021.
    5. Jun, Doobae & Ku, Hyejin, 2015. "Static hedging of chained-type barrier options," The North American Journal of Economics and Finance, Elsevier, vol. 33(C), pages 317-327.
    6. Paul Ormerod, 2010. "La crisis actual y la culpabilidad de la teoría macroeconómica," Revista de Economía Institucional, Universidad Externado de Colombia - Facultad de Economía, vol. 12(22), pages 111-128, January-J.
    7. An Chen & Thai Nguyen & Thorsten Sehner, 2022. "Unit-Linked Tontine: Utility-Based Design, Pricing and Performance," Risks, MDPI, vol. 10(4), pages 1-27, April.
    8. Kearney, Fearghal & Shang, Han Lin & Sheenan, Lisa, 2019. "Implied volatility surface predictability: The case of commodity markets," Journal of Banking & Finance, Elsevier, vol. 108(C).
    9. Boyarchenko, Svetlana & Levendorskii[caron], Sergei, 2007. "Optimal stopping made easy," Journal of Mathematical Economics, Elsevier, vol. 43(2), pages 201-217, February.
    10. Robert C. Merton, 2006. "Paul Samuelson and Financial Economics," The American Economist, Sage Publications, vol. 50(2), pages 9-31, October.
    11. Eduardo Abi Jaber, 2022. "The characteristic function of Gaussian stochastic volatility models: an analytic expression," Working Papers hal-02946146, HAL.
    12. Peter Carr & Liuren Wu, 2014. "Static Hedging of Standard Options," The Journal of Financial Econometrics, Society for Financial Econometrics, vol. 12(1), pages 3-46.
    13. Ammann, Manuel & Kind, Axel & Wilde, Christian, 2003. "Are convertible bonds underpriced? An analysis of the French market," Journal of Banking & Finance, Elsevier, vol. 27(4), pages 635-653, April.
    14. Jeremy Leake, 2003. "Credit spreads on sterling corporate bonds and the term structure of UK interest rates," Bank of England working papers 202, Bank of England.
    15. Suleyman Basak & Georgy Chabakauri, 2012. "Dynamic Hedging in Incomplete Markets: A Simple Solution," Review of Financial Studies, Society for Financial Studies, vol. 25(6), pages 1845-1896.
    16. Jay Cao & Jacky Chen & John Hull & Zissis Poulos, 2021. "Deep Hedging of Derivatives Using Reinforcement Learning," Papers 2103.16409, arXiv.org.
    17. Kuang, Yu Flora & Qin, Bo, 2009. "Performance-vested stock options and interest alignment," The British Accounting Review, Elsevier, vol. 41(1), pages 46-61.
    18. Dubey, Pradeep & Sondermann, Dieter, 2009. "Perfect competition in an oligopoly (including bilateral monopoly)," Games and Economic Behavior, Elsevier, vol. 65(1), pages 124-141, January.
    19. Saphores, J.D. & Khalaf, L. & Pelletier, D., 2000. "On Jumps and ARCH Effects in Natural Resource Prices. An Application to Stumpage Prices from Pacific Northwest National Forests," Papers 00-03, Laval - Recherche en Energie.
    20. Cui, Yiran & del Baño Rollin, Sebastian & Germano, Guido, 2017. "Full and fast calibration of the Heston stochastic volatility model," European Journal of Operational Research, Elsevier, vol. 263(2), pages 625-638.

    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:phsmap:v:534:y:2019:i:c:s0378437119313573. 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: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.