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

Grunspan, Cyril

doi:10.2139/ssrn.1965977

Abstract

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

Cyril Grunspan

Ecole Superieure d'Ingenierie Leonard de Vinci (ESILV)

November 29, 2011

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.

Number of Pages in PDF File: 18

Keywords: smile asymptotics, implied lognormal volatility

JEL Classification: G12, G13, C65

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Date posted: November 29, 2011 ; Last revised: December 6, 2011

Suggested Citation

Grunspan, Cyril, Asymptotic Expansions of the Lognormal Implied Volatility: A Model Free Approach (November 29, 2011). Available at SSRN: http://ssrn.com/abstract=1965977 or http://dx.doi.org/10.2139/ssrn.1965977

Contact Information

Cyril Grunspan (Contact Author)

Ecole Superieure d'Ingenierie Leonard de Vinci (ESILV) ( email )

92916 Paris La Defense Cedex
France