In this paper, we study stochastic volatility models in regimes where the
maturity is small but large compared to the mean-reversion time of the
stochastic volatility factor. The problem falls in the class of
averaging/homogenization problems for nonlinear HJB type equations where the
"fast variable" lives in a non-compact space. We develop a general argument
based on viscosity solutions which we apply to the two regimes studied in the
paper.