  Empirical studies have emphasized that the equity implied volatility is
characterized by a negative skew inversely proportional to the square root of
the time-to-maturity. We examine the short-time-to-maturity behavior of the
implied volatility smile for pure jump exponential additive processes. An
excellent calibration of the equity volatility surfaces has been achieved by a
class of these additive processes with power-law scaling. The two power-law
scaling parameters are $\beta$, related to the variance of jumps, and $\delta$,
related to the smile asymmetry. It has been observed, in option market data,
that $\beta=1$ and $\delta=-1/2$. In this paper, we prove that the implied
volatility of these additive processes is consistent, in the short-time, with
the equity market empirical characteristics if and only if $\beta=1$ and
$\delta=-1/2$.
