  We consider the class of self-similar Gaussian stochastic volatility models,
and compute the small-time (near-maturity) asymptotics for the corresponding
asset price density, the call and put pricing functions, and the implied
volatilities. Unlike the well-known model-free behavior for extreme-strike
asymptotics, small-time behaviors of the above depend heavily on the model, and
require a control of the asset price density which is uniform with respect to
the asset price variable, in order to translate into results for call prices
and implied volatilities. Away from the money, we express the asymptotics
explicitly using the volatility process' self-similarity parameter $H$, its
first Karhunen-Loeve eigenvalue at time 1, and the latter's multiplicity.
Several model-free estimators for $H$ result. At the money, a separate study is
required: the asymptotics for small time depend instead on the integrated
variance's moments of orders 1/2 and 3/2, and the estimator for $H$ sees an
affine adjustment, while remaining model-free.
