英文标题：
《Realized volatility and parametric estimation of Heston SDEs》
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作者：
Robert Azencott and Peng Ren and Ilya Timofeyev
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最新提交年份：
2020
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英文摘要：
  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.
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中文摘要：
我们对赫斯顿SDE基于矩的参数估值器进行了详细的分析，这些参数估值器共同推动了收益率R\\u t$和平方波动率V\\u t$。由于波动率不可直接观测，我们的参数估计量是根据已实现波动率的经验矩$Y\\u t$构建的，当然，这些波动率是可观测的。已实现的波动率是在大小为$\\ varepsilon$的滑动窗口上计算的，并划分为$J（\\ varepsilon）$区间。我们建立了联合选择$J（\\ varepsilon）$和回报率数据的次抽样频率的标准。我们得到了已实现波动率到真实波动率的$L^q$收敛速度的显式界，即$\\变ε\\到0$。反过来，这些界限也提供了赫斯顿波动率SDE参数的可观测估计值的L^q$收敛速度。我们的理论分析得到了联合Heston SDE广泛数值模拟的补充，以研究基于矩的参数估值器的实际性能。我们的结果为将赫斯顿SDEs参数与观察到的股价序列充分拟合提供了实用指南。
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Computational Finance        计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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一级分类：Mathematics        数学
二级分类：Probability        概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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