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

作者：Gulisashvili Archil^*; Stein Elias M

来源：Applied Mathematics and Optimization, 2010, 61(3): 287-315.

DOI：10.1007/s00245-009-9085-x

• Stein-Stein model
• Heston model
• Mixing distribution density
• Stock price
• Bessel processes
• Ornstein-Uhlenbeck processes
• CIR processes
• Asymptotic formulas
• Implied volatility

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.

• 出版日期2010-6