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The implied volatility skew has received relatively little attention in theliterature on short-term asymptotics for financial models with jumps, despiteits importance in model selection and calibration. We rectify this by providinghigh-order asymptotic expansions for the at-the-money implied volatility skew,under a rich class of stochastic volatility models with independent stable-likejumps of infinite variation. The case of a pure-jump stable-like L\'evy modelis also considered under the minimal possible conditions for the resultingexpansion to be well defined. Unlike recent results for "near-the-money" optionprices and implied volatility, the results herein aid in understanding how theimplied volatility smile near expiry is affected by important features of thecontinuous component, such as the leverage and vol-of-vol parameters. Asintermediary results we obtain high-order expansions for at-the-money digitalcall option prices, which furthermore allow us to infer analogous results forthe delta of at-the-money options. Simulation results indicate that ourasymptotic expansions give good fits for options with maturities up to onemonth, underpinning their relevance in practical applications, and an analysisof the implied volatility skew in recent S&P500 options data shows it to beconsistent with the infinite variation jump component of our models.

Short-time asymptotics for the implied volatility skew under a stochastic volatility model with L\'evy jumps