IDEAS home Printed from https://ideas.repec.org/a/wsi/ijtafx/v07y2004i06ns0219024904002669.html
   My bibliography  Save this article

Adaptive Finite Element Methods For Local Volatility European Option Pricing

Author

Listed:
  • ALEXANDRE ERN

    (CERMICS, Ecole nationale des ponts et chaussées, 6 et 8 avenue Blaise Pascal, 77455 Marne la Vallée cedex 2, France)

  • STÉPHANE VILLENEUVE

    (Université d'Evry Val d'Essonne, Equipe d'Analyse et de Probabilité, Boulevard F. Mitterand, 91 025 Evry cedex, France)

  • ANTONINO ZANETTE

    (Dipartimento di Finanza dell'Impresa, e dei Mercati Finanziari, Università di Udine, via Tomadini 30/A, Udine, Italy)

Abstract

We investigate finite element discretizations using functions that are discontinuous in time and continuous in space for European options with local volatility Black–Scholes models. We present ana posteriorierror estimate where a user-specified functional of the error is controlled by the inner product of the finite element residual with the solution of a dual problem that involves the density of the target functional as prescribed data. Examples of error functionals are discussed in the context of either option pricing or volatility calibration from market data. Thea posteriorierror estimator is then localized onto the space-time cells of the computational mesh and implemented in the framework of an adaptive mesh refinement/derefinement algorithm which provides some form of optimal compromise between accuracy requirements and computational costs. Numerical examples illustrate the efficiency of the proposed methodology.

Suggested Citation

  • Alexandre Ern & Stéphane Villeneuve & Antonino Zanette, 2004. "Adaptive Finite Element Methods For Local Volatility European Option Pricing," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 7(06), pages 659-684.
    • Handle: RePEc:wsi:ijtafx:v:07:y:2004:i:06:n:s0219024904002669
    DOI: 10.1142/S0219024904002669
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0219024904002669
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0219024904002669?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:wsi:ijtafx:v:07:y:2004:i:06:n:s0219024904002669. 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: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/ijtaf/ijtaf.shtml .

    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.