IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-0-8176-8180-7_7.html

Optimal Quantization Methods and Applications to Numerical Problems in Finance

In: Handbook of Computational and Numerical Methods in Finance

Author

Listed:
  • Gilles Pagès

    (Université Paris 6, Laboratoire de Probabilités et Modèles Aléatoires CNRS, UMR 7599)

  • Huyên Pham

    (Université Paris 6, Laboratoire de Probabilités et Modèles Aléatoires CNRS, UMR 7599)

  • Jacques Printems

    (Université Paris 12, Centre de Mathématiques Faculté de Sciences et Technologie CNRS, UMR 8050)

Abstract

We review optimal quantization methods for numerically solving nonlinear problems in higher dimensions associated with Markov processes. Quantization of a Markov process consists in a spatial discretization on finite grids optimally fitted to the dynamics of the process. Two quantization methods are proposed: the first one, called marginal quantization, relies on an optimal approximation of the marginal distributions of the process, while the second one, called Markovian quantization, looks for an optimal approximation of transition probabilities of the Markov process at some points. Optimal grids and their associated weights can be computed by a stochastic gradient descent method based on Monte Carlo simulations. We illustrate this optimal quantization approach with four numerical applications arising in finance: European option pricing, optimal stopping problems and American option pricing, stochastic control problems and mean-variance hedging of options and filtering in stochastic volatility models.

Suggested Citation

  • Gilles Pagès & Huyên Pham & Jacques Printems, 2004. "Optimal Quantization Methods and Applications to Numerical Problems in Finance," Springer Books, in: Svetlozar T. Rachev (ed.), Handbook of Computational and Numerical Methods in Finance, chapter 7, pages 253-297, Springer.
    • Handle: RePEc:spr:sprchp:978-0-8176-8180-7_7
    DOI: 10.1007/978-0-8176-8180-7_7
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    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:sprchp:978-0-8176-8180-7_7. 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.