IDEAS home Printed from https://ideas.repec.org/a/wsi/ijtafx/v09y2006i06ns0219024906003834.html
   My bibliography  Save this article

Pricing Of First Touch Digitals Under Normal Inverse Gaussian Processes

Author

Listed:
  • OLEG KUDRYAVTSEV

    (Department of Informatics, Russian Customs Academy Rostov Branch, Budennovskiy 20, Rostov-on-Don, 344011, Russia)

  • SERGEI LEVENDORSKIǏ

    (Department of Economics, University of Texas at Austin, 1 University Station C3100, Austin, TX 78712, USA)

Abstract

We calculate prices of first touch digitals under normal inverse Gaussian (NIG) processes, and compare them to prices in the Brownian model and double exponential jump-diffusion model. Numerical results are produced to show that for typical parameters values, the relative error of the Brownian motion approximation to NIG price can be 2–3 dozen percent if the spot price is at the distance 0.05–0.2 from the barrier (normalized to one). A similar effect is observed for approximations by the double exponential jump-diffusion model, if the jump component of the approximation is significant. We show that two jump-diffusion processes can give approximately the same results for European options but essentially different results for first touch digitals and barrier options. A fast approximate pricing formula under NIG is derived.

Suggested Citation

  • Oleg Kudryavtsev & Sergei Levendorskiǐ, 2006. "Pricing Of First Touch Digitals Under Normal Inverse Gaussian Processes," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 9(06), pages 915-949.
    • Handle: RePEc:wsi:ijtafx:v:09:y:2006:i:06:n:s0219024906003834
    DOI: 10.1142/S0219024906003834
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0219024906003834
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0219024906003834?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:09:y:2006:i:06:n:s0219024906003834. 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.