IDEAS home Printed from https://ideas.repec.org/a/wly/jnlmpe/v2023y2023i1n4669161.html

Numerical Method for American Option Pricing under the Time‐Fractional Black–Scholes Model

Author

Listed:
  • Yesen Sun
  • Wenxiu Gong
  • Hongliang Dai
  • Long Yuan

Abstract

The fractional Black–Scholes model has had limited applications in financial markets. Instead, the time‐fractional Black–Scholes equation has attracted much research interest. However, it is difficult to obtain the analytic expression for American option pricing under the time‐fractional Black–Scholes model. This paper will present an operator‐splitting method to price the American options under the time‐fractional Black–Scholes model. The fractional partial differential complementarity problem (FPDCP) that the American option price satisfied is split into two subproblems: a linear boundary value problem and an algebraic system. A high‐order compact (HOC) scheme and a grid stretching (GS) method are considered for the linear boundary problem. Furthermore, numerical results show that the HOC scheme with a GS method gives an accurate numerical solution for American options under the time‐fractional Black–Scholes model.

Suggested Citation

  • Yesen Sun & Wenxiu Gong & Hongliang Dai & Long Yuan, 2023. "Numerical Method for American Option Pricing under the Time‐Fractional Black–Scholes Model," Mathematical Problems in Engineering, John Wiley & Sons, vol. 2023(1).
    • Handle: RePEc:wly:jnlmpe:v:2023:y:2023:i:1:n:4669161
    DOI: 10.1155/2023/4669161
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2023/4669161
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2023/4669161?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
    ---><---

    References listed on IDEAS

    as
    1. Bertram During & Michel Fourni'e, 2014. "High-order compact finite difference scheme for option pricing in stochastic volatility models," Papers 1404.5140, arXiv.org.
    2. Samuli Ikonen & Jari Toivanen, 2007. "Componentwise Splitting Methods For Pricing American Options Under Stochastic Volatility," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 10(02), pages 331-361.
    3. Maryam Safaei & Abodolsadeh Neisy & Nader Nematollahi, 2018. "New Splitting Scheme for Pricing American Options Under the Heston Model," Computational Economics, Springer;Society for Computational Economics, vol. 52(2), pages 405-420, August.
    4. Bertram Düring & Michel Fournié & Ansgar Jüngel, 2003. "High Order Compact Finite Difference Schemes for a Nonlinear Black-Scholes Equation," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 6(07), pages 767-789.
    5. Bertram During & Michel Fourni'e & Christof Heuer, 2014. "High-order compact finite difference schemes for option pricing in stochastic volatility models on non-uniform grids," Papers 1404.5138, arXiv.org.
    6. Brennan, Michael J & Schwartz, Eduardo S, 1977. "The Valuation of American Put Options," Journal of Finance, American Finance Association, vol. 32(2), pages 449-462, May.
    7. Yuri M. Dimitrov & Lubin G. Vulkov, 2016. "High order finite difference schemes on non-uniform meshes for the time-fractional Black-Scholes equation," Papers 1604.05178, arXiv.org.
    8. 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. Oleksandr Zhylyevskyy, 2010. "A fast Fourier transform technique for pricing American options under stochastic volatility," Review of Derivatives Research, Springer, vol. 13(1), pages 1-24, April.
    2. Bertram During & Alexander Pitkin, 2017. "High-order compact finite difference scheme for option pricing in stochastic volatility jump models," Papers 1704.05308, arXiv.org, revised Feb 2019.
    3. Kozpınar, Sinem & Uzunca, Murat & Karasözen, Bülent, 2020. "Pricing European and American options under Heston model using discontinuous Galerkin finite elements," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 177(C), pages 568-587.
    4. Karel in 't Hout & Jari Toivanen, 2015. "Application of Operator Splitting Methods in Finance," Papers 1504.01022, arXiv.org.
    5. 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.
    6. Joao Felipe Gueiros & Hemanth Chandravamsi & Steven H. Frankel, 2025. "Deep Learning vs. Black-Scholes: Option Pricing Performance on Brazilian Petrobras Stocks," Papers 2504.20088, arXiv.org.
    7. Giandomenico, Rossano, 2006. "Valuing an American Put Option," MPRA Paper 20082, University Library of Munich, Germany.
    8. José Daniel López Barrientos & Ana Pamela Flores Herrera & Ernesto Fernández Arias & Beatris Adriana Escobedo Trujillo, 2025. "Proposals to Transfer Risks in Avocado Load," Remef - Revista Mexicana de Economía y Finanzas Nueva Época REMEF (The Mexican Journal of Economics and Finance), Instituto Mexicano de Ejecutivos de Finanzas, IMEF, vol. 20(2), pages 1-29, Abril - J.
    9. Engstrom, Malin & Norden, Lars, 2000. "The early exercise premium in American put option prices," Journal of Multinational Financial Management, Elsevier, vol. 10(3-4), pages 461-479, December.
    10. Pressacco, Flavio & Gaudenzi, Marcellino & Zanette, Antonino & Ziani, Laura, 2008. "New insights on testing the efficiency of methods of pricing and hedging American options," European Journal of Operational Research, Elsevier, vol. 185(1), pages 235-254, February.
    11. Jérôme Detemple, 2014. "Optimal Exercise for Derivative Securities," Annual Review of Financial Economics, Annual Reviews, vol. 6(1), pages 459-487, December.
    12. In oon Kim & Bong-Gyu Jang & Kyeong Tae Kim, 2013. "A simple iterative method for the valuation of American options," Quantitative Finance, Taylor & Francis Journals, vol. 13(6), pages 885-895, May.
    13. Suresh M. Sundaresan, 2000. "Continuous‐Time Methods in Finance: A Review and an Assessment," Journal of Finance, American Finance Association, vol. 55(4), pages 1569-1622, August.
    14. Li, Chenxu & Ye, Yongxin, 2019. "Pricing and Exercising American Options: an Asymptotic Expansion Approach," Journal of Economic Dynamics and Control, Elsevier, vol. 107(C), pages 1-1.
    15. Hadjiyannakis, Steve & Culumovic, Louis & Welch, Robert L., 1998. "The relative mispricing of the constant variance American put model," International Review of Economics & Finance, Elsevier, vol. 7(2), pages 149-171.
    16. Luca Vincenzo Ballestra, 2018. "Fast and accurate calculation of American option prices," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 41(2), pages 399-426, November.
    17. Qianru Shang & Brian Byrne, 2021. "American option pricing: Optimal Lattice models and multidimensional efficiency tests," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 41(4), pages 514-535, April.
    18. Luna Rigby & Rudiger Frey & Erik Schlogl, 2026. "If Not Now, Then When? Model Risk in the Optimal Exercise of American Options," Papers 2603.19984, arXiv.org.
    19. Darae Jeong & Minhyun Yoo & Changwoo Yoo & Junseok Kim, 2019. "A Hybrid Monte Carlo and Finite Difference Method for Option Pricing," Computational Economics, Springer;Society for Computational Economics, vol. 53(1), pages 111-124, January.
    20. Jiří Hozman & Tomáš Tichý & Hana Dvořáčková, 2024. "Valuation of mining projects under dynamic model framework," Annals of Operations Research, Springer, vol. 337(3), pages 1167-1204, June.

    More about this item

    Statistics

    Access and download statistics

    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:wly:jnlmpe:v:2023:y:2023:i:1:n:4669161. 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: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/2629 .

    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.