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

The implied volatility slope has received relatively little attention in the literature on short-time asymptotics for financial models with jumps, despite its importance in model selection and calibration. In this paper, we fill this gap by providing high-order asymptotic expansions for the at-the-money implied volatility slope of 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. As an intermediary result, we also obtain high-order expansions for at-the-money digital call option prices. The results obtained herein are remarkably different from those obtained in recent papers close-to-the-money option prices in that they aid in understanding how the behavior of implied volatility near expiry is affected by important model parameters, such as the leverage and vol vol parameters, that were not present in the aforementioned earlier results. Our simulation results also indicate that for parameter values of relevance in finance, the asymptotic expansions give a good fit for maturities up to one month.