Small-maturity asymptotics for the at-the-money implied volatility slope in L\'evy models

30 May 2016  ·  Gerhold Stefan, Gülüm I. Cetin, Pinter Arpad ·

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. read more

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