IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v23y1995i1p53-61.html
   My bibliography  Save this article

An example in which the Lugannani-Rice saddlepoint formula fails

Author

Listed:
  • Booth, James G.
  • Wood, Andrew T. A.

Abstract

In almost all documented applications, the normal-based Lugannani and Rice (1980) formula provides an extremely accurate approximation to tail probabilities. However, it would be wrong to conclude that this formula is always reliable. In the present paper, we consider an example, the first passage time of a random walk with drift, in which the overall performance of the normal-based Lugannani and Rice formula is rather poor. In contrast, a modified Lugannani and Rice formula, in which the normal base is replaced by an inverse Gaussian base, gives an excellent approximation. A similar modification of Barndorff-Nielsen's (1986) formula is also considered. The main focus of this paper is on a detailed study of the approximations in the extreme right tail of the distribution, and our theoretical results go some of the way towards explaining the observed numerical behaviour. However, on closer scrutiny, there is a disconcerting lack of correspondence between some of the theoretical limits and the numerical results, which appears to be due to convergence rates of some quantities being extremely slow.

Suggested Citation

  • Booth, James G. & Wood, Andrew T. A., 1995. "An example in which the Lugannani-Rice saddlepoint formula fails," Statistics & Probability Letters, Elsevier, vol. 23(1), pages 53-61, April.
    • Handle: RePEc:eee:stapro:v:23:y:1995:i:1:p:53-61
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0167-7152(94)00094-O
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

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


    Cited by:

    1. J. ANNAERT & Crispiniano Garcia Joao Batista & J. LAMOOT & G. LANINE, 2006. "Don’t Fall from the Saddle: the Importance of Higher Moments of Credit Loss Distributions," Working Papers of Faculty of Economics and Business Administration, Ghent University, Belgium 06/367, Ghent University, Faculty of Economics and Business Administration.

    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:eee:stapro:v:23:y:1995:i:1:p:53-61. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.