title: Small-Maturity Asymptotics for the At-The-Money Implied Volatility Slope in Lévy Models.
abstract: We consider the at-the-money (ATM) strike derivative of implied volatility as the maturity tends to zero. Our main results quantify the behaviour of the slope for infinite activity exponential Lévy models including a Brownian component. As auxiliary results, we obtain asymptotic expansions of short maturity ATM digital call options, using Mellin transform asymptotics. Finally, we discuss when the ATM slope is consistent with the steepness of the smile wings, as given by Lee's moment formula.
authors.affiliation: Institute of Statistics and Mathematical Methods in Economics, TU Wien , Wiedner Hauptstrasse 8-10/E105-1, Vienna A-1040 , Austria.
authors.forename: Stefan
authors.initials: S
authors.lastname: Gerhold
authors.affiliation: Institute of Statistics and Mathematical Methods in Economics, TU Wien , Wiedner Hauptstrasse 8-10/E105-1, Vienna A-1040 , Austria.
authors.forename: I Cetin
authors.initials: IC
authors.lastname: Gülüm
authors.affiliation: Institute of Statistics and Mathematical Methods in Economics, TU Wien , Wiedner Hauptstrasse 8-10/E105-1, Vienna A-1040 , Austria.
authors.forename: Arpad
authors.initials: A
authors.lastname: Pinter
keywords: Implied volatility; Lévy process; Mellin transform; asymptotics; digital option