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Small-maturity asymptotics for the at-the-money implied volatility slope in Lévy models (1310.3061v3)

Published 11 Oct 2013 in q-fin.PR

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.

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