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Small-Maturity Asymptotics for the At-The-Money Implied Volatility Slope in Lévy Models
Stefan Gerhold1, I Cetin Gülüm1, Arpad Pinter1
1Institute of Statistics and Mathematical Methods in Economics, TU Wien , Wiedner Hauptstrasse 8-10/E105-1, Vienna A-1040 , Austria.
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.
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