IDEAS home Printed from https://ideas.repec.org/p/arx/papers/0809.3305.html
   My bibliography  Save this paper

Implied volatility explosions: European calls and implied volatilities close to expiry in exponential L\'evy models

Author

Listed:
  • Michael Roper

Abstract

We examine the small expiry behaviour of European call options in stock price models of exponential L\'evy type. In most cases of interest, we are able to identify the exact small expiry asymptotics. In "complete generality" we are able to show that the time value of the call option has O(\tau) decay as \tau (time to expiry) goes to zero. Using our results on the behaviour of call options close to expiry we show that implied volatility explodes as $\tau\to0^+$ in "most" exponential L\'evy models. Attention is restricted to calls and implied volatilities that are not at-the-money.

Suggested Citation

  • Michael Roper, 2008. "Implied volatility explosions: European calls and implied volatilities close to expiry in exponential L\'evy models," Papers 0809.3305, arXiv.org, revised Sep 2008.
    • Handle: RePEc:arx:papers:0809.3305
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/0809.3305
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Sergei Levendorskii, 2004. "The American put and European options near expiry, under Levy processes," Papers cond-mat/0404103, arXiv.org.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. René Carmona & Sergey Nadtochiy, 2011. "Tangent Models As A Mathematical Framework For Dynamic Calibration," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(01), pages 107-135.
    2. Leif Andersen & Alexander Lipton, 2012. "Asymptotics for Exponential Levy Processes and their Volatility Smile: Survey and New Results," Papers 1206.6787, arXiv.org.
    3. Leif Andersen & Alexander Lipton, 2013. "Asymptotics For Exponential Lévy Processes And Their Volatility Smile: Survey And New Results," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 16(01), pages 1-98.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Elizondo Rocío & Padilla Pablo & Bladt Mogens, 2009. "An Alternative Formula to Price American Options," Working Papers 2009-06, Banco de México.
    2. Leif Andersen & Alexander Lipton, 2013. "Asymptotics For Exponential Lévy Processes And Their Volatility Smile: Survey And New Results," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 16(01), pages 1-98.
    3. Leif Andersen & Alexander Lipton, 2012. "Asymptotics for Exponential Levy Processes and their Volatility Smile: Survey and New Results," Papers 1206.6787, arXiv.org.

    More about this item

    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:0809.3305. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc 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 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.