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
复制标题
随机波动率模型中股票价格分布密度和隐含波动率的渐近行为
DOI：
10.1007/s00245-009-9085-x
复制
发表时间：
2009
影响因子：
1.8
通讯作者：
E. Stein
中科院分区：
文献类型：
--
作者：
Archil Gulisashvili;E. Stein
研究了具有随机波动的股票价格模型中分布密度的渐近行为。本文的主要研究对象是斯坦-斯坦模型和赫斯顿模型中波动率平方过程的时间平均密度和股票价格过程的密度。我们在这些密度的渐近展开式中找到了前导项的显式公式，并给出了误差估计。作为结果的一个应用，得到了Stein-Stein模型和Heston模型中隐含波动率的尖锐渐近公式。
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.