Small-maturity asymptotics for the at-the-money implied volatility slope in Lévy models

2013/10/11 by Stefan Gerhold, Gerhold, Stefan, I. Cetin Gülüm +3
Economics, Econometrics and Finance · #41A60 #44A15 #60G51 #91G20 #FOS: Economics and business #Pricing of Securities (q-fin.PR) #msc:41A60 #msc:44A15 #msc:60G51 #msc:91G20 #q-fin.PR

paper · pdf · doi:10.48550/arxiv.1310.3061

arxiv created 2016/05/30 · arxiv updated 2016/05/31

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 Lévy 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.

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