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

Asymptotic Behavior of the Stock Price Distribution Density and Implied Volatility in Stochastic Volatility Models