  In this paper, we study a family of stochastic volatility processes; this
family features a mean reversion term for the volatility and a double CEV-like
exponent that generalizes SABR and Heston's models. We derive approximated
closed form formulas for the digital prices, the local and implied
volatilities. Our formulas are efficient for small maturities.
  Our method is based on differential geometry, especially small time
diffusions on riemanian spaces. This geometrical point of view can be extended
to other processes, and is very accurate to produce variate smiles for small
maturities and small moneyness.
