IDEAS home Printed from https://ideas.repec.org/a/hin/jnlmpe/1052084.html
   My bibliography  Save this article

On the Convergence of a Crank–Nicolson Fitted Finite Volume Method for Pricing American Bond Options

Author

Listed:
  • Xiaoting Gan
  • Dengguo Xu

Abstract

This paper develops and analyses a Crank–Nicolson fitted finite volume method to price American options on a zero-coupon bond under the Cox–Ingersoll–Ross (CIR) model governed by a partial differential complementarity problem (PDCP). Based on a penalty approach, the PDCP results in a nonlinear partial differential equation (PDE). We then apply a fitted finite volume method for the spatial discretization along with a Crank–Nicolson time-stepping scheme for the PDE, which results in a nonlinear algebraic equation. We show that this scheme is consistent, stable, and monotone, and hence, the convergence of the numerical solution to the viscosity solution of the continuous problem is guaranteed. To solve the system of nonlinear equations effectively, an iterative algorithm is established and its convergence is proved. Numerical experiments are presented to demonstrate the accuracy, efficiency, and robustness of the new numerical method.

Suggested Citation

  • Xiaoting Gan & Dengguo Xu, 2020. "On the Convergence of a Crank–Nicolson Fitted Finite Volume Method for Pricing American Bond Options," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-13, May.
    • Handle: RePEc:hin:jnlmpe:1052084
    DOI: 10.1155/2020/1052084
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/MPE/2020/1052084.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/MPE/2020/1052084.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2020/1052084?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
    ---><---

    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:hin:jnlmpe:1052084. 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: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.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.