IDEAS home Printed from https://ideas.repec.org/a/kap/compec/v67y2026i6d10.1007_s10614-025-11025-9.html

Stability and Error Estimates of Operator Splitting Methods on a Variable Space-Time Grid for American Options with Jumps

Author

Listed:
  • Pradeep Kumar Sahu

    (Indian Institute of Technology Patna, Department of Mathematics)

  • Kuldip Singh Patel

    (Indian Institute of Technology Patna, Department of Mathematics)

  • Pawan Kumar Mishra

    (Indian Institute of Technology Bhilai, Department of Mathematics)

Abstract

This article presents three different variable space-time grid operator splitting (OS) methods for pricing American option under jump-diffusion model. The temporal semi-discretization is done using variable time step implicit-explicit backward difference OS (BDF-OS), Crank-Nicolson OS (CN-OS), and midpoint OS (MP-OS) methods. A priori stability analysis is performed for each semi-discrete method and error estimates are established. The space discretization is performed using the variable space step finite difference approximations. The numerical illustrations for Merton’s and Kou’s jump-diffusion models are performed. The BDF-OS method is demonstrated to be first-order accurate in time and second-order accurate in space variable, while the CN-OS and MP-OS methods are second-order accurate in both the variables. The impact of the variable space-time grid is shown via error plots.

Suggested Citation

  • Pradeep Kumar Sahu & Kuldip Singh Patel & Pawan Kumar Mishra, 2026. "Stability and Error Estimates of Operator Splitting Methods on a Variable Space-Time Grid for American Options with Jumps," Computational Economics, Springer;Society for Computational Economics, vol. 67(6), pages 4389-4422, June.
    • Handle: RePEc:kap:compec:v:67:y:2026:i:6:d:10.1007_s10614-025-11025-9
    DOI: 10.1007/s10614-025-11025-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10614-025-11025-9
    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/s10614-025-11025-9?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

    for a different version of it.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;

    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:kap:compec:v:67:y:2026:i:6:d:10.1007_s10614-025-11025-9. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.