Small-maturity asymptotics for the at-the-money implied volatility slope in L\'evy models
Pricing of Securities
2016-05-31 v3
Abstract
We consider the at-the-money strike derivative of implied volatility as the maturity tends to zero. Our main results quantify the behavior of the slope for infinite activity exponential L\'evy models including a Brownian component. As auxiliary results, we obtain asymptotic expansions of short maturity at-the-money digital call options, using Mellin transform asymptotics. Finally, we discuss when the at-the-money slope is consistent with the steepness of the smile wings, as given by Lee's moment formula.
Keywords
Cite
@article{arxiv.1310.3061,
title = {Small-maturity asymptotics for the at-the-money implied volatility slope in L\'evy models},
author = {Stefan Gerhold and I. Cetin Gülüm and Arpad Pinter},
journal= {arXiv preprint arXiv:1310.3061},
year = {2016}
}