IDEAS home Printed from
   My bibliography  Save this paper

A Note on the Equivalence between the Normal and the Lognormal Implied Volatility : A Model Free Approach


  • Cyril Grunspan


First, we show that implied normal volatility is intimately linked with the incomplete Gamma function. Then, we deduce an expansion on implied normal volatility in terms of the time-value of a European call option. Then, we formulate an equivalence between the implied normal volatility and the lognormal implied volatility with any strike and any model. This generalizes a known result for the SABR model. Finally, we adress the issue of the "breakeven move" of a delta-hedged portfolio.

Suggested Citation

  • Cyril Grunspan, 2011. "A Note on the Equivalence between the Normal and the Lognormal Implied Volatility : A Model Free Approach," Papers 1112.1782,
  • Handle: RePEc:arx:papers:1112.1782

    Download full text from publisher

    File URL:
    File Function: Latest version
    Download Restriction: no

    References listed on IDEAS

    1. Cyril Grunspan, 2011. "Asymptotic Expansions of the Lognormal Implied Volatility : A Model Free Approach," Papers 1112.1652,
    2. Jaehyuk Choi & Kwangmoon Kim & Minsuk Kwak, 2009. "Numerical Approximation of the Implied Volatility Under Arithmetic Brownian Motion," Applied Mathematical Finance, Taylor & Francis Journals, vol. 16(3), pages 261-268.
    3. S. Benaim & P. Friz, 2009. "Regular Variation And Smile Asymptotics," Mathematical Finance, Wiley Blackwell, vol. 19(1), pages 1-12.
    4. Marco Avellaneda & Sasha Stoikov, 2008. "High-frequency trading in a limit order book," Quantitative Finance, Taylor & Francis Journals, vol. 8(3), pages 217-224.
    5. Jörg Kienitz & Manuel Wittke, 2010. "Option Valuation in Multivariate SABR Models," Research Paper Series 272, Quantitative Finance Research Centre, University of Technology, Sydney.
    6. Walter Schachermayer & Josef Teichmann, 2008. "How Close Are The Option Pricing Formulas Of Bachelier And Black-Merton-Scholes?," Mathematical Finance, Wiley Blackwell, vol. 18(1), pages 155-170.
    7. Viorel Costeanu & Dan Pirjol, 2011. "Asymptotic Expansion for the Normal Implied Volatility in Local Volatility Models," Papers 1105.3359,
    8. Roger W. Lee, 2004. "The Moment Formula For Implied Volatility At Extreme Strikes," Mathematical Finance, Wiley Blackwell, vol. 14(3), pages 469-480.
    Full references (including those not matched with items on IDEAS)


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

    Cited by:

    1. Louis-Pierre Arguin & Nien-Lin Liu & Tai-Ho Wang, 2017. "Most-likely-path in Asian option pricing under local volatility models," Papers 1706.02408,
    2. Dan Pirjol & Lingjiong Zhu, 2016. "Short Maturity Asian Options in Local Volatility Models," Papers 1609.07559,
    3. Christian Bayer & Juho Happola & Ra'ul Tempone, 2017. "Implied Stopping Rules for American Basket Options from Markovian Projection," Papers 1705.00558,, revised Jun 2017.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:


    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:arx:papers:1112.1782. 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). 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.

    If CitEc recognized a 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.

    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.