  We consider a stochastic volatility asset price model in which the volatility
is the absolute value of a continuous Gaussian process with arbitrary
prescribed mean and covariance. By exhibiting a Karhunen-Lo\`{e}ve expansion
for the integrated variance, and using sharp estimates of the density of a
general second-chaos variable, we derive asymptotics for the asset price
density for large or small values of the variable, and study the wing behavior
of the implied volatility in these models. Our main result provides explicit
expressions for the first five terms in the expansion of the implied
volatility. The expressions for the leading three terms are simple, and based
on three basic spectral-type statistics of the Gaussian process: the top
eigenvalue of its covariance operator, the multiplicity of this eigenvalue, and
the $L^{2}$ norm of the projection of the mean function on the top eigenspace.
The fourth term requires knowledge of all eigen-elements. We present detailed
numerics based on realistic liquidity assumptions in which classical and
long-memory volatility models are calibrated based on our expansion.
