  The implied volatility skew has received relatively little attention in the
literature on short-term asymptotics for financial models with jumps, despite
its importance in model selection and calibration. We rectify this by providing
high-order asymptotic expansions for the at-the-money implied volatility skew,
under a rich class of stochastic volatility models with independent stable-like
jumps of infinite variation. The case of a pure-jump stable-like L\'evy model
is also considered under the minimal possible conditions for the resulting
expansion to be well defined. Unlike recent results for "near-the-money" option
prices and implied volatility, the results herein aid in understanding how the
implied volatility smile near expiry is affected by important features of the
continuous component, such as the leverage and vol-of-vol parameters. As
intermediary results we obtain high-order expansions for at-the-money digital
call option prices, which furthermore allow us to infer analogous results for
the delta of at-the-money options. Simulation results indicate that our
asymptotic expansions give good fits for options with maturities up to one
month, underpinning their relevance in practical applications, and an analysis
of the implied volatility skew in recent S&P500 options data shows it to be
consistent with the infinite variation jump component of our models.
