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

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

2011-12-07

arxiv.org/abs/1112.1652v1

Economy

Quantitative Finance

Pricing of Securities

18 pages

Scientific paper

We invert the Black-Scholes formula. We consider the cases low strike, large
strike, short maturity and large maturity. We give explicitly the ?rst 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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