[go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/a/spr/finsto/v3y1999i4p391-412.html
   My bibliography  Save this article

Applications of Malliavin calculus to Monte Carlo methods in finance

Author

Listed:
  • Eric Fournié

    (PARIBAS Capital Markets, 10 Harewood Avenue, London NW1 6AA, United Kingdom)

  • Jean-Michel Lasry

    (PARIBAS Capital Markets, 10 Harewood Avenue, London NW1 6AA, United Kingdom)

  • Pierre-Louis Lions

    (CEREMADE, Université Paris IX Dauphine, Place du Maréchal de Lattre de Tassigny, F-75775 Paris Cedex 16, France)

  • Jérôme Lebuchoux

    (CEREMADE, Université Paris IX Dauphine, Place du Maréchal de Lattre de Tassigny, F-75775 Paris Cedex 16, France)

  • Nizar Touzi

    (CEREMADE, Université Paris IX Dauphine, Place du Maréchal de Lattre de Tassigny, F-75775 Paris Cedex 16, France)

Abstract
This paper presents an original probabilistic method for the numerical computations of Greeks (i.e. price sensitivities) in finance. Our approach is based on the {\it integration-by-parts} formula, which lies at the core of the theory of variational stochastic calculus, as developed in the Malliavin calculus. The Greeks formulae, both with respect to initial conditions and for smooth perturbations of the local volatility, are provided for general discontinuous path-dependent payoff functionals of multidimensional diffusion processes. We illustrate the results by applying the formula to exotic European options in the framework of the Black and Scholes model. Our method is compared to the Monte Carlo finite difference approach and turns out to be very efficient in the case of discontinuous payoff functionals.

Suggested Citation

  • Eric Fournié & Jean-Michel Lasry & Pierre-Louis Lions & Jérôme Lebuchoux & Nizar Touzi, 1999. "Applications of Malliavin calculus to Monte Carlo methods in finance," Finance and Stochastics, Springer, vol. 3(4), pages 391-412.
    • Handle: RePEc:spr:finsto:v:3:y:1999:i:4:p:391-412
    Note: received: July 1997; final version received: September 1998
    as

    Download full text from publisher

    File URL: http://link.springer.de/link/service/journals/00780/papers/9003004/90030391.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

    Monte Carlo methods; Malliavin calculus; hedge ratios and Greeks;
    All these keywords.

    JEL classification:

    • 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:3:y:1999:i:4:p:391-412. 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.