标题： 已实现波动率和Heston SDE的参数估计 显示英文标题

标题： Realized volatility and parametric estimation of Heston SDEs

摘要： 我们对驱动收益率$R_t$和平方波动率$V_t$的 Heston SDEs 的\emph{可观察的}矩方法参数估计量进行了详细分析。 由于波动率不可直接观测，我们的参数估计量是基于可观察的已实现波动率$Y_t$的经验矩构建的。 已实现波动率是在大小为$\varepsilon$的滑动窗口内计算的，这些窗口被划分为$J(\varepsilon)$个区间。 我们建立了联合选择$J(\varepsilon)$和收益率数据子采样频率的标准。 我们得到当$\varepsilon \to 0$时，实现波动率收敛到真实波动率的$L^q$的显式界限。 这些界限也提供了我们可观测估计量对于 Heston 波动率 SDE 参数的收敛速度$L^q$。 我们的理论分析通过联合 Heston SDE 的大量数值模拟得到补充，以研究基于矩的方法估计量的实际性能。 我们的结果为适当拟合 Heston SDE 参数到观测股票价格序列提供了实用指南。 显示英文摘要

摘要： We present a detailed analysis of \emph{observable} moments based parameter estimators for the Heston SDEs jointly driving the rate of returns $R_t$ and the squared volatilities $V_t$. Since volatilities are not directly observable, our parameter estimators are constructed from empirical moments of realized volatilities $Y_t$, which are of course observable. Realized volatilities are computed over sliding windows of size $\varepsilon$, partitioned into $J(\varepsilon)$ intervals. We establish criteria for the joint selection of $J(\varepsilon)$ and of the sub-sampling frequency of return rates data. We obtain explicit bounds for the $L^q$ speed of convergence of realized volatilities to true volatilities as $\varepsilon \to 0$. In turn, these bounds provide also $L^q$ speeds of convergence of our observable estimators for the parameters of the Heston volatility SDE. Our theoretical analysis is supplemented by extensive numerical simulations of joint Heston SDEs to investigate the actual performances of our moments based parameter estimators. Our results provide practical guidelines for adequately fitting Heston SDEs parameters to observed stock prices series.