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

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

2009-06-01

arxiv.org/abs/0906.0392v1

Economy

Quantitative Finance

Pricing of Securities

21pages

Scientific paper

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.

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