IDEAS home Printed from https://ideas.repec.org/a/kap/compec/v64y2024i2d10.1007_s10614-023-10441-z.html
   My bibliography  Save this article

A Hybrid Spectral-Finite Difference Method for Numerical Pricing of Time-Fractional Black–Scholes Equation

Author

Listed:
  • Nasibeh Mollahasani

    (Graduate University of Advanced Technology)

Abstract

In this paper, option pricing through introducing a novel hybrid method for solving time-fractional Black–Scholes equation is considered. The presented method is based on time and space discretization. Time discretization is according to a second order finite difference formula. Space discretization is done by a spectral method based on fractional order shifted Hahn functions (FOSHFs) and an operational process by defining fractional order Hahn operational matrices. Convergence and error analysis for FOSHFs approximation and also for the proposed method are discussed. For validating obtained theoretical results and demonstrating the accuracy, convergency and efficiency of the method, two numerical examples with the known exact solutions are considerd and compared to other methods. Furthermore, the presented method is used to price three different European options governed by a time-fractional Black–Scholes model: European call option, European put option and European double barrier knock-out call option.

Suggested Citation

  • Nasibeh Mollahasani, 2024. "A Hybrid Spectral-Finite Difference Method for Numerical Pricing of Time-Fractional Black–Scholes Equation," Computational Economics, Springer;Society for Computational Economics, vol. 64(2), pages 841-869, August.
    • Handle: RePEc:kap:compec:v:64:y:2024:i:2:d:10.1007_s10614-023-10441-z
    DOI: 10.1007/s10614-023-10441-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10614-023-10441-z
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10614-023-10441-z?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. Mohammadi, Hakimeh & Kumar, Sunil & Rezapour, Shahram & Etemad, Sina, 2021. "A theoretical study of the Caputo–Fabrizio fractional modeling for hearing loss due to Mumps virus with optimal control," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    2. Panas, E., 2001. "Long memory and chaotic models of prices on the London Metal Exchange," Resources Policy, Elsevier, vol. 27(4), pages 235-246, December.
    3. Fenghua Wen & Zhifeng Liu, 2009. "A Copula-Based Correlation Measure And Its Application In Chinese Stock Market," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 8(04), pages 787-801.
    4. 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)

    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. Nuugulu, Samuel M & Gideon, Frednard & Patidar, Kailash C, 2021. "A robust numerical scheme for a time-fractional Black-Scholes partial differential equation describing stock exchange dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    2. 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.
    3. Filipe Fontanela & Antoine Jacquier & Mugad Oumgari, 2019. "A Quantum algorithm for linear PDEs arising in Finance," Papers 1912.02753, arXiv.org, revised Feb 2021.
    4. Weihan Li & Jin E. Zhang & Xinfeng Ruan & Pakorn Aschakulporn, 2024. "An empirical study on the early exercise premium of American options: Evidence from OEX and XEO options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 44(7), pages 1117-1153, July.
    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. Thomas Kokholm & Martin Stisen, 2015. "Joint pricing of VIX and SPX options with stochastic volatility and jump models," Journal of Risk Finance, Emerald Group Publishing Limited, vol. 16(1), pages 27-48, January.
    7. 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.
    8. 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.
    9. 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).
    10. Boyarchenko, Svetlana & Levendorskii[caron], Sergei, 2007. "Optimal stopping made easy," Journal of Mathematical Economics, Elsevier, vol. 43(2), pages 201-217, February.
    11. Robert C. Merton, 2006. "Paul Samuelson and Financial Economics," The American Economist, Sage Publications, vol. 50(2), pages 9-31, October.
    12. Eduardo Abi Jaber, 2022. "The characteristic function of Gaussian stochastic volatility models: an analytic expression," Working Papers hal-02946146, HAL.
    13. Peter Carr & Liuren Wu, 2014. "Static Hedging of Standard Options," Journal of Financial Econometrics, Oxford University Press, vol. 12(1), pages 3-46.
    14. 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.
    15. 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.
    16. Suleyman Basak & Georgy Chabakauri, 2012. "Dynamic Hedging in Incomplete Markets: A Simple Solution," The Review of Financial Studies, Society for Financial Studies, vol. 25(6), pages 1845-1896.
    17. Jay Cao & Jacky Chen & John Hull & Zissis Poulos, 2021. "Deep Hedging of Derivatives Using Reinforcement Learning," Papers 2103.16409, arXiv.org.
    18. Kuang, Yu Flora & Qin, Bo, 2009. "Performance-vested stock options and interest alignment," The British Accounting Review, Elsevier, vol. 41(1), pages 46-61.
    19. 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.
    20. 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.

    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:kap:compec:v:64:y:2024:i:2:d:10.1007_s10614-023-10441-z. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.