We consider the at-the-money strike derivative of implied volatility as the maturity tends to zero. Our main results quantify the growth of the slope for infinite activity exponential Levy models . As auxiliary results, we obtain the limiting values of short maturity  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.
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.
R
growth
behavior
R
Levy models
L\'evy models including a Brownian component
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the limiting values
asymptotic expansions
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at-the-money