Advanced Search
MyIDEAS: Login to save this paper or follow this series

Asymptotic Expansion for the Normal Implied Volatility in Local Volatility Models

Contents:

Author Info

  • Viorel Costeanu
  • Dan Pirjol
Registered author(s):

    Abstract

    We study the dynamics of the normal implied volatility in a local volatility model, using a small-time expansion in powers of maturity T. At leading order in this expansion, the asymptotics of the normal implied volatility is similar, up to a different definition of the moneyness, to that of the log-normal volatility. This relation is preserved also to order O(T) in the small-time expansion, and differences with the log-normal case appear first at O(T^2). The results are illustrated on a few examples of local volatility models with analytical local volatility, finding generally good agreement with exact or numerical solutions. We point out that the asymptotic expansion can fail if applied naively for models with nonanalytical local volatility, for example which have discontinuous derivatives. Using perturbation theory methods, we show that the ATM normal implied volatility for such a model contains a term ~ \sqrt{T}, with a coefficient which is proportional with the jump of the derivative.

    Download Info

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
    File URL: http://arxiv.org/pdf/1105.3359
    File Function: Latest version
    Download Restriction: no

    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1105.3359.

    as in new window
    Length:
    Date of creation: May 2011
    Date of revision:
    Handle: RePEc:arx:papers:1105.3359

    Contact details of provider:
    Web page: http://arxiv.org/

    Related research

    Keywords:

    This paper has been announced in the following NEP Reports:

    References

    No references listed on IDEAS
    You can help add them by filling out this form.

    Citations

    Lists

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    Statistics

    Access and download statistics

    Corrections

    When requesting a correction, please mention this item's handle: RePEc:arx:papers:1105.3359. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (arXiv administrators).

    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.

    If references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link to it, you can help with 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 profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.