  We consider a stochastic volatility model which captures relevant stylized
facts of financial series, including the multi-scaling of moments. The
volatility evolves according to a generalized Ornstein-Uhlenbeck processes with
super-linear mean reversion.
  Using large deviations techniques, we determine the asymptotic shape of the
implied volatility surface in any regime of small maturity $t \to 0$ or extreme
log-strike $|\kappa| \to \infty$ (with bounded maturity). Even if the price has
continuous paths, out-of-the-money implied volatility diverges for small
maturity, producing a very pronounced smile.
