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Asymptotic Expansions of the Lognormal Implied Volatility : A Model Free Approach

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  • Cyril Grunspan

Abstract

We invert the Black-Scholes formula. We consider the cases low strike, large strike, short maturity and large maturity. We give explicitly the first 5 terms of the expansions. A method to compute all the terms by induction is also given. At the money, we have a closed form formula for implied lognormal volatility in terms of a power series in call price.

Suggested Citation

  • Cyril Grunspan, 2011. "Asymptotic Expansions of the Lognormal Implied Volatility : A Model Free Approach," Papers 1112.1652, arXiv.org.
  • Handle: RePEc:arx:papers:1112.1652
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    File URL: http://arxiv.org/pdf/1112.1652
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    Cited by:

    1. Cyril Grunspan & Joris Van Der Hoeven, 2017. "Effective asymptotic analysis for finance," Working Papers hal-01573621, HAL.
    2. Cyril Grunspan, 2011. "A Note on the Equivalence between the Normal and the Lognormal Implied Volatility : A Model Free Approach," Papers 1112.1782, arXiv.org.

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