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Implied Volatility at Expiration


  • Alexey Medvedev

    (PhD student, Swiss Finance Institute and University of Geneva)


The main result of the paper is a formula for zero time-to-maturity limit of implied volatilities of European options under a broad class of stochastic volatility models. Based on this formula, we propose a closed-form approximation of the implied volatility smile. Numerical examples suggest that our approximation is accurate in the absence of mean-reversion in stochastic volatility.

Suggested Citation

  • Alexey Medvedev, 2004. "Implied Volatility at Expiration," Swiss Finance Institute Research Paper Series 08-04, Swiss Finance Institute, revised Jan 2008.
  • Handle: RePEc:chf:rpseri:rp0804

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    Cited by:

    1. Itkin, Andrey, 2015. "To sigmoid-based functional description of the volatility smile," The North American Journal of Economics and Finance, Elsevier, vol. 31(C), pages 264-291.
    2. Cristian Homescu, 2011. "Implied Volatility Surface: Construction Methodologies and Characteristics," Papers 1107.1834,

    More about this item


    Option pricing; stochastic volatility; implied volatility; short-maturity asymptotics.;

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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