IDEAS home Printed from https://ideas.repec.org/a/kap/compec/v65y2025i4d10.1007_s10614-024-10625-1.html
   My bibliography  Save this article

Pricing Convertible Bonds with the Penalty TF Model Using Finite Element Method

Author

Listed:
  • Rakhymzhan Kazbek

    (Nazarbayev University)

  • Yogi Erlangga

    (Zayed University)

  • Yerlan Amanbek

    (Nazarbayev University)

  • Dongming Wei

    (Nazarbayev University)

Abstract

In this paper, we discuss finite element methods (FEM) for solving numerically the so-called TF model, a PDE-based model for pricing convertible bonds. The model consists of two coupled Black-Scholes equations, whose solutions are constrained. The construction of the FEM is based on the P1 and P2 element, applied to the penalty-based reformulation of the TF model. The resultant nonlinear differential algebraic equations are solved using a modified Crank-Nicolson scheme, with non-linear part with non-smooth terms solved at each time step by Newton’s method. While P1-FEM demonstrates a comparable convergence rate to the standard finite difference method, a better convergence rate is achieved with P2-FEM. The fast convergence of P2-FEM leads to a significant reduction in CPU time, due to the reduction in the number of elements used to achieve the same accuracy as P1-FEM or FDM. As the Greeks are important numerical parameters in the bond pricing, we compute some Greeks using the computed solution and the corresponding FEM approximation functions.

Suggested Citation

  • Rakhymzhan Kazbek & Yogi Erlangga & Yerlan Amanbek & Dongming Wei, 2025. "Pricing Convertible Bonds with the Penalty TF Model Using Finite Element Method," Computational Economics, Springer;Society for Computational Economics, vol. 65(4), pages 1971-1998, April.
    • Handle: RePEc:kap:compec:v:65:y:2025:i:4:d:10.1007_s10614-024-10625-1
    DOI: 10.1007/s10614-024-10625-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10614-024-10625-1
    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/s10614-024-10625-1?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.

    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:65:y:2025:i:4:d:10.1007_s10614-024-10625-1. 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.