  We study the asymptotic behavior of distribution densities arising in stock
price models with stochastic volatility. The main objects of our interest in
the present paper are the density of time averages of the squared volatility
process and the density of the stock price process in the Stein-Stein and the
Heston model. We find explicit formulas for leading terms in asymptotic
expansions of these densities and give error estimates. As an application of
our results, sharp asymptotic formulas for the implied volatility in the
Stein-Stein and the Heston model are obtained.
