IDEAS home Printed from
   My bibliography  Save this article

Option Hedging And Implied Volatilities In A Stochastic Volatility Model


  • Eric Renault
  • Nizar Touzi


In the stochastic volatility framework of Hull and White (1987), we characterize the so-called Black and Scholes implied volatility as a function of two arguments the ratio of the strike to the underlying asset price and the instantaneous value of the volatility By studying the variation m the first argument, we show that the usual hedging methods, through the Black and Scholes model, lead to an underhedged (resp. overhedged) position for in-the-money (resp out-of the-money) options, and a perfect partial hedged position for at the-money options These results are shown to be closely related to the "smile effect", which is proved to be a natural consequence of the stochastic volatility feature the deterministic dependence of the implied volatility on the underlying volatility process suggests the use of implied volatility data for the estimation of the parameters of interest A statistical procedure of filtering (of the latent volatility process) and estimation (of its parameters) is shown to be strongly consistent and asymptotically normal. Copyright 1996 Blackwell Publishers.

Suggested Citation

  • Eric Renault & Nizar Touzi, 1996. "Option Hedging And Implied Volatilities In A Stochastic Volatility Model," Mathematical Finance, Wiley Blackwell, vol. 6(3), pages 279-302.
  • Handle: RePEc:bla:mathfi:v:6:y:1996:i:3:p:279-302

    Download full text from publisher

    File URL:
    File Function: link to full text
    Download Restriction: Access to full text is restricted to subscribers.

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

    More about this item


    Access and download statistics


    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:bla:mathfi:v:6:y:1996:i:3:p:279-302. 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: (Wiley-Blackwell Digital Licensing) or (Christopher F. Baum). General contact details of provider: .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.