IDEAS home Printed from https://ideas.repec.org/a/spr/finsto/v6y2002i4p449-471.html
   My bibliography  Save this article

An analysis of a least squares regression method for American option pricing

Author

Listed:
  • Philip Protter

    (Operations Research and Industrial Engineering Department, Cornell University, Ithaca, NY 14853-3801, USA Manuscript)

  • Emmanuelle Clément

    (Équipe d'Analyse et de mathématiques appliquées, Université de Marne-la-Vallée, 5 Bld Descartes, Champs-sur-marne, 77454 Marne-la-Vallée Cedex 2, France)

  • Damien Lamberton

    (Équipe d'Analyse et de mathématiques appliquées, Université de Marne-la-Vallée, 5 Bld Descartes, Champs-sur-marne, 77454 Marne-la-Vallée Cedex 2, France)

Abstract

Recently, various authors proposed Monte-Carlo methods for the computation of American option prices, based on least squares regression. The purpose of this paper is to analyze an algorithm due to Longstaff and Schwartz. This algorithm involves two types of approximation. Approximation one: replace the conditional expectations in the dynamic programming principle by projections on a finite set of functions. Approximation two: use Monte-Carlo simulations and least squares regression to compute the value function of approximation one. Under fairly general conditions, we prove the almost sure convergence of the complete algorithm. We also determine the rate of convergence of approximation two and prove that its normalized error is asymptotically Gaussian.

Suggested Citation

  • Philip Protter & Emmanuelle Clément & Damien Lamberton, 2002. "An analysis of a least squares regression method for American option pricing," Finance and Stochastics, Springer, vol. 6(4), pages 449-471.
    • Handle: RePEc:spr:finsto:v:6:y:2002:i:4:p:449-471
    Note: received: April 2001; final version received: January 2002
    as

    Download full text from publisher

    File URL: http://link.springer.de/link/service/journals/00780/papers/2006004/20060449.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

    American options; optimal stopping; Monte-Carlo methods; least squares regression;
    All these keywords.

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • 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:6:y:2002:i:4:p:449-471. 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.