IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1311.4698.html
   My bibliography  Save this paper

A central limit theorem for Latin hypercube sampling with dependence and application to exotic basket option pricing

Author

Listed:
  • Christoph Aistleitner
  • Markus Hofer
  • Robert Tichy

Abstract

We consider the problem of estimating $\mathbb{E} [f(U^1, \ldots, U^d)]$, where $(U^1, \ldots, U^d)$ denotes a random vector with uniformly distributed marginals. In general, Latin hypercube sampling (LHS) is a powerful tool for solving this kind of high-dimensional numerical integration problem. In the case of dependent components of the random vector $(U^1, \ldots, U^d)$ one can achieve more accurate results by using Latin hypercube sampling with dependence (LHSD). We state a central limit theorem for the $d$-dimensional LHSD estimator, by this means generalising a result of Packham and Schmidt. Furthermore we give conditions on the function $f$ and the distribution of $(U^1, \ldots, U^d)$ under which a reduction of variance can be achieved. Finally we compare the effectiveness of Monte Carlo and LHSD estimators numerically in exotic basket option pricing problems.

Suggested Citation

  • Christoph Aistleitner & Markus Hofer & Robert Tichy, 2013. "A central limit theorem for Latin hypercube sampling with dependence and application to exotic basket option pricing," Papers 1311.4698, arXiv.org.
    • Handle: RePEc:arx:papers:1311.4698
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1311.4698
    File Function: Latest version
    Download Restriction: no
    ---><---

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:arx:papers:1311.4698. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.