We consider a stochastic volatility model which captures relevant stylized facts of financial series, including the multiscaling of moments.  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, we show that out-of-the-money implied volatility diverges for small maturity, producing a very pronounced smile . When |\kappa| is much larger than t, the implied volatility is asymptotically an explicit function of just the ratio (\kappa / t) .
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 .
R
multiscaling
multi-scaling
A
The volatility evolves according to a generalized Ornstein-Uhlenbeck processes with super-linear mean reversion.
D
we show that
D
. When |\kappa| is much larger than t, the implied volatility is asymptotically an explicit function of just the ratio (\kappa / t)