IDEAS home Printed from https://ideas.repec.org/a/spr/finsto/v28y2024i1d10.1007_s00780-023-00525-x.html
   My bibliography  Save this article

Arbitrage problems with reflected geometric Brownian motion

Author

Listed:
  • Dean Buckner

    (The Eumaeus Project)

  • Kevin Dowd

    (Durham University Business School)

  • Hardy Hulley

    (University of Technology Sydney)

Abstract

Contrary to the claims made by several authors, a financial market model in which the price of a risky security follows a reflected geometric Brownian motion is not arbitrage-free. In fact, such models violate even the weakest no-arbitrage condition considered in the literature. Consequently, they do not admit numéraire portfolios or equivalent risk-neutral probability measures, which makes them unsuitable for contingent claim valuation. Unsurprisingly, the published option pricing formulae for such models violate classical no-arbitrage bounds.

Suggested Citation

  • Dean Buckner & Kevin Dowd & Hardy Hulley, 2024. "Arbitrage problems with reflected geometric Brownian motion," Finance and Stochastics, Springer, vol. 28(1), pages 1-26, January.
    • Handle: RePEc:spr:finsto:v:28:y:2024:i:1:d:10.1007_s00780-023-00525-x
    DOI: 10.1007/s00780-023-00525-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00780-023-00525-x
    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/s00780-023-00525-x?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.

    More about this item

    Keywords

    Reflected geometric Brownian motion; Arbitrage; Local time; Contingent claim valuation;
    All these keywords.

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

    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:28:y:2024:i:1:d:10.1007_s00780-023-00525-x. 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.