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

Published 7 Dec 2011 in q-fin.PR | (1112.1652v1)

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.

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Cyril Grunspan

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