Asymptotic Expansions of the Lognormal Implied Volatility: A Model Free Approach
Ecole Superieure d'Ingenierie Leonard de Vinci (ESILV)
November 29, 2011
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
Date posted: November 29, 2011 ; Last revised: December 6, 2011