The asymptotic smile of a multiscaling stochastic volatility model

Abstract

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→0 or extreme log-strike |κ|→∞ (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.