IDEAS home Printed from https://ideas.repec.org/a/taf/quantf/v2y2002i6p415-431.html
   My bibliography  Save this article

A theory of non-Gaussian option pricing

Author

Listed:
  • Lisa Borland

Abstract

Option pricing formulae are derived from a non-Gaussian model of stock returns. Fluctuations are assumed to evolve according to a nonlinear Fokker-Planck equation which maximizes the Tsallis nonextensive entropy of index q. A generalized form of the Black-Scholes differential equation is found, and we derive a martingale measure which leads to closed-form solutions for European call options. The standard Black-Scholes pricing equations are recovered as a special case (q = 1). The distribution of stock returns is well modelled with q circa 1.5. Using that value of q in the option pricing model we reproduce the volatility smile. The partial derivatives (or Greeks) of the model are also calculated. Empirical results are demonstrated for options on Japanese Yen futures. Using just one value of σ across strikes we closely reproduce market prices, for expiration times ranging from weeks to several months.

Suggested Citation

  • Lisa Borland, 2002. "A theory of non-Gaussian option pricing," Quantitative Finance, Taylor & Francis Journals, vol. 2(6), pages 415-431.
    • Handle: RePEc:taf:quantf:v:2:y:2002:i:6:p:415-431
    DOI: 10.1080/14697688.2002.0000009
    as

    Download full text from publisher

    File URL: http://www.tandfonline.com/doi/abs/10.1080/14697688.2002.0000009
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/14697688.2002.0000009?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

    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:taf:quantf:v:2:y:2002:i:6:p:415-431. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/RQUF20 .

    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.