Nothing Special   »   [go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/p/chf/rpseri/rp1954.html
   My bibliography  Save this paper

Weighted Monte Carlo with Least Squares and Randomized Extended Kaczmarz for Option Pricing

Author

Listed:
  • Damir Filipović

    (Ecole Polytechnique Fédérale de Lausanne; Swiss Finance Institute)

  • Kathrin Glau

    (Queen Mary University of London)

  • Yuji Nakatsukasa

    (University of Oxford)

  • Francesco Statti

    (Ecole Polytechnique Fédérale de Lausanne)

Abstract
We propose a methodology for computing single and multi-asset European option prices, and more generally expectations of scalar functions of (multivariate) random variables. This new approach combines the ability of Monte Carlo simulation to handle high-dimensional problems with the efficiency of function approximation. Specifically, we first generalize the recently developed method for multivariate integration in [arXiv:1806.05492] to integration with respect to probability measures. The method is based on the principle “approximate and integrate” in three steps i) sample the integrand at points in the integration domain, ii) approximate the integrand by solving a least-squares problem, iii) integrate the approximate function. In high-dimensional applications we face memory limitations due to large storage requirements in step ii). Combining weighted sampling and the randomized extended Kaczmarz algorithm we obtain a new efficient approach to solve large-scale least-squares problems. Our convergence and cost analysis along with numerical experiments show the effectiveness of the method in both low and high dimensions, and under the assumption of a limited number of available simulations.

Suggested Citation

  • Damir Filipović & Kathrin Glau & Yuji Nakatsukasa & Francesco Statti, 2019. "Weighted Monte Carlo with Least Squares and Randomized Extended Kaczmarz for Option Pricing," Swiss Finance Institute Research Paper Series 19-54, Swiss Finance Institute.
    • Handle: RePEc:chf:rpseri:rp1954
    as

    Download full text from publisher

    File URL: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3471164
    Download Restriction: no
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Lotfi Boudabsa & Damir Filipović, 2022. "Machine learning with kernels for portfolio valuation and risk management," Finance and Stochastics, Springer, vol. 26(2), pages 131-172, April.

    More about this item

    Keywords

    sMonte Carlo; Monte Carlo under budget constraints; variance reduction; multi-asset options; Kaczmarz algorithm; weighted sampling; large-scale least-squares problems;
    All these keywords.

    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:chf:rpseri:rp1954. 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: Ridima Mittal (email available below). General contact details of provider: https://edirc.repec.org/data/fameech.html .

    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.