IDEAS home Printed from https://ideas.repec.org/a/spr/finsto/v5y2001i3p343-355.html
   My bibliography  Save this article

Fractional Brownian motion, random walks and binary market models

Author

Listed:
  • Tommi Sottinen

    (Department of Mathematics, University of Helsinki, P.O. Box 4, 00014 Helsinki, Finland Manuscript)

Abstract

We prove a Donsker type approximation theorem for the fractional Brownian motion in the case $H>1/2.$ Using this approximation we construct an elementary market model that converges weakly to the fractional analogue of the Black-Scholes model. We show that there exist arbitrage opportunities in this model. One such opportunity is constructed explicitly.

Suggested Citation

  • Tommi Sottinen, 2001. "Fractional Brownian motion, random walks and binary market models," Finance and Stochastics, Springer, vol. 5(3), pages 343-355.
    • Handle: RePEc:spr:finsto:v:5:y:2001:i:3:p:343-355
    Note: received: October 1999; final version received: August 2000
    as

    Download full text from publisher

    File URL: http://link.springer.de/link/service/journals/00780/papers/1005003/10050343.pdf
    Download Restriction: Access to the full text of the articles in this series is restricted
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    More about this item

    Keywords

    Fractional Brownian motion; random walk; stock price model; binary market model;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

    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:spr:finsto:v:5:y:2001:i:3:p:343-355. 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.