英文标题：
《Distributions of Historic Market Data -- Relaxation and Correlations》
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作者：
M. Dashti Moghaddam, Zhiyuan Liu and R. A. Serota
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最新提交年份：
2020
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英文摘要：
We investigate relaxation and correlations in a class of mean-reverting models for stochastic variances. We derive closed-form expressions for the correlation functions and leverage for a general form of the stochastic term. We also discuss correlation functions and leverage for three specific models -- multiplicative, Heston (Cox-Ingersoll-Ross) and combined multiplicative-Heston -- whose steady-state probability density functions are Gamma, Inverse Gamma and Beta Prime respectively, the latter two exhibiting \"fat\" tails. For the Heston model, we apply the eigenvalue analysis of the Fokker-Planck equation to derive the correlation function -- in agreement with the general analysis -- and to identify a series of time scales, which are observable in relaxation of cumulants on approach to the steady state. We test our findings on a very large set of historic financial markets data.
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中文摘要：
我们研究了一类随机方差均值回复模型中的松弛和相关性。我们推导了相关函数的闭式表达式，并利用了随机项的一般形式。我们还讨论了三种特定模型的相关函数和杠杆作用——乘法、Heston（Cox Ingersoll Ross）和组合乘法Heston——其稳态概率密度函数分别为Gamma、逆Gamma和Beta素数，后两种模型显示出“胖”尾。对于赫斯顿模型，我们应用福克-普朗克方程的特征值分析来推导相关函数（与一般分析一致），并确定一系列时间尺度，这些时间尺度在接近稳态时的累积量松弛过程中可以观察到。我们在一组非常大的历史金融市场数据上检验了我们的发现。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Statistical Finance 统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
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一级分类：Quantitative Finance 数量金融学
二级分类：Mathematical Finance 数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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