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

Grunspan, Cyril

doi:10.2139/ssrn.1965977

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

18 Pages Posted: 29 Nov 2011 Last revised: 6 Dec 2011

See all articles by Cyril Grunspan

Cyril Grunspan

Ecole Superieure d'Ingenierie Leonard de Vinci (ESILV)

Date Written: 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.

Keywords: smile asymptotics, implied lognormal volatility

JEL Classification: G12, G13, C65

Suggested Citation: Suggested Citation

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