IDEAS home Printed from https://ideas.repec.org/a/spr/finsto/v2y1998i4p369-397.html
   My bibliography  Save this article

Option pricing with transaction costs and a nonlinear Black-Scholes equation

Author

Listed:
  • Halil Mete Soner

    (Department of Mathematics, Carnegie Mellon University, Pittsburgh, PA 15213, USA)

  • Guy Barles

    (FacultÊ des Sciences et Techniques, UniversitÊ de Tours, Parc de Grandmont, F-37200 Tours, France)

Abstract

In a market with transaction costs, generally, there is no nontrivial portfolio that dominates a contingent claim. Therefore, in such a market, preferences have to be introduced in order to evaluate the prices of options. The main goal of this article is to quantify this dependence on preferences in the specific example of a European call option. This is achieved by using the utility function approach of Hodges and Neuberger together with an asymptotic analysis of partial differential equations. We are led to a nonlinear Black-Scholes equation with an adjusted volatility which is a function of the second derivative of the price itself. In this model, our attitude towards risk is summarized in one free parameter a which appears in the nonlinear Black-Scholes equation : we provide an upper bound for the probability of missing the hedge in terms of a and the magnitude of the proportional transaction cost which shows the connections between this parameter a and the risk.

Suggested Citation

  • Halil Mete Soner & Guy Barles, 1998. "Option pricing with transaction costs and a nonlinear Black-Scholes equation," Finance and Stochastics, Springer, vol. 2(4), pages 369-397.
    • Handle: RePEc:spr:finsto:v:2:y:1998:i:4:p:369-397
    Note: received: March 1996; final version received: May 1997
    as

    Download full text from publisher

    File URL: http://link.springer.de/link/service/journals/00780/papers/8002004/80020369.pdf
    Download Restriction: Access to the full text of the articles in this series is restricted
    File URL: http://link.springer.de/link/service/journals/00780/papers/8002004/80020369.ps.gz
    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

    Transaction costs; options; viscosity solutions; dynamic programming;
    All these keywords.

    JEL classification:

    • D52 - Microeconomics - - General Equilibrium and Disequilibrium - - - Incomplete Markets
    • 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:2:y:1998:i:4:p:369-397. 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.