几种Copula函数在沪深股市相关性建模中的应用

研究了Copula函数对沪深股市的相关性建模问题.许多学者用Gaussian Copula建模,但是它无法捕捉到尾部变化,尾部相关系数不存在.用t-Copula度量中国股市的相关性,捕捉到了尾部变化,并计算出了尾部相关系数,克服了Gaussian Copula对相关性建模的不足,并通过AIC准则比较得到t-Copula优于Gaussian Copula.最后对3种Archimedean Copula进行比较,通过比较它们与经验分布函数的距离,说明Gumble Copula更加适用于中国的金融市场.     

相关系数矩阵与多元线性相关分析

相关系数指度量两个随机变量间线性关系的无量纲指标,在研究了相关系数矩阵性质及其与多元随机变量线性相关性之间关系的基础上,提出多元线性相关系数的定义,用于衡量多个变鼋间线性相关强弱的无量纲指标.分析表明,所提多元线性相关系数能够较全面地反映变量间的线性相关强度.     

沪深300指数与沪深股市尾部相关性分析

根据沪深股市非线性的特征,利用Kendall秩相关系数与Copula函数之间的关系,对Copula函数的参数进行估计.选择Gumbel Copula、Clayton Copula和Frank Copula来度量上证综指、深证综指和沪深300指数之间的尾部相关性.实证结果分析,Clayton Copula函数能较好的度量出三个指数之间具有较强的下尾相关性,且进行量化后的相关性能够较好刻画股票市场的变化.     

基于Copula模型的尾部相依性长记忆效应研究

在已有动态Copula模型基础上,提出可同时描述尾部相依性的非对称和长记忆特征的Copula模型.基于沪深股市数据,首次从尾部相依性的角度检验了沪深股市的长记忆效应.研究发现,沪深两市在重大利好或利空消息冲击时的相关性(即尾部相依性)都具有长记忆效应,极端事件对尾部相依性的影响比对未来收益和波动的影响更加持久.而且,样本外分析结果表明,相比已有Copula模型,具有长记忆性的Copula模型能更准确地预测未来1周至1年的市场间相关性.     

基于Copula函数和非参数估计的尾部相关性

给出基于Copula函数的尾部相关性的定义和性质,采用非参数方法估计尾部相关系数.结合数据得出上证指数和深圳指数的尾部相关系数和对应图形比较,可知两种股票的上尾比下尾相关性强.此相关系数反映了上证指数与深圳指数在极端值处同时小于或同时大于某个数值的概率大小.     

股票收益率尾部相关性的Copula度量及模拟

股票收益率尾部相关性是研究金融市场关联性的重要内容.由于传统的τ、ρ等相关系数是对随机变量的全局度量,不适合用于收益率分布尾部这种局部特征的相关性度量.因此,在引入左尾(右尾)相关系数的基础上,讨论了它们的Copula度量及其相关性质.最后,通过计算机模拟分析了沪、深股指收益率尾部相关性的变化趋势,有效避免了Copula模型的设定困难,并得到了尾部相关性增强、相关不对称等结论.     

Copula模型在沪深股市相关性研究中的应用

本文利用沪深股票市场数据,研究了二者之间的相关结构,尤其是尾部相关情况。由于股票收益率序列存在着条件自相关和条件异方差,为避免这些对Copula参数估计的影响,我们先对收益率序列进行AR(4)-GJRGARCH(1,1)-t建模,得到的标准化残差经BDS检验为独立同分布(i.i.d.)序列,再进行Copula建模。实证结果表明,沪深股市存在很强的正相关性,以及对称的尾部相关。这与大多数国外学者认为股票市场之间存在非对称相关现象的结论不同。本文通过图形检测和解析方法相结合来选择对数据拟合最好的Copula函数,结果表明学生t-Copula可以很好地刻画沪深股市的相关性。     

关于相关系数的探讨

讨论统计学中的线性相关系数和非线性相关系数,寻找其共性.对比研究与信息再利用.得到一个相关系数的通用公式.该公式适合于统计学中的各种数据处理.     

平稳序列BMM模型与沪深股市极端风险研究

基于VaR理论正态分布假设导致的尾部风险低估问题,研究了GEV分布下的BMM模型及区间关联下的极值VaR的建模,并实证分析了沪深股市极端风险.研究结果表明:BMM模型对金融风险的厚尾具有更合理的理论基础.然而,涨跌停板极大地抑制了沪深股市极值数据的异质性,形成"极值不极"现象,导致在较高置信度下BMM模型更为有效,而在较低置信度下反而存在低估问题,有效性尚不及VaR模型.     

沪深港股市相关性的小波分析

主要使用离散小波变换(DW T)对沪深港股市的相关性进行研究.小波可以把方差和相关系数在不同尺度上进行分解,以便更仔细地研究时间序列的波动性在不同尺度上的相关程度.研究发现:三地股票市场的波动性都随着小波尺度的变化而变化;沪深股市与香港股市相关性非常低,而且在不同尺度上相关程度有较大差别.     

Multivariate conditional versions of Spearman's rho and related measures of tail dependence

A new family of conditional-dependence measures based on Spearman's rho is introduced. The corresponding multidimensional versions are established. Asymptotic distributional results are derived for related estimators which are based on the empirical copula. Particular emphasis is placed on a new type of multidimensional tail-dependence measure and its relationship to other measures of tail dependence is shown. Multivariate tail dependence describes the limiting amount of dependence in the vertices of the copula's domain.     

基于时变SJC-Copula对商品期货市场间风险传染的探究

分别选取WIND商品指数和CRB指数作为衡量我国商品期货市场及国际商品期货市场综合价格的指标,利用时变SJC-Copula模型构建两者之间的动态相依结构,通过动态的尾部相关系数来探究我国商品期货市场与国际市场间的尾部相关性.实证结果表明,我国商品期货市场与国际市场间的上尾相关性要强于下尾相关性,即当商品期货价格上涨时,两个市场间更易发生风险传染.     

A copula entropy approach to correlation measurement at the country level

The entropy optimization approach has widely been applied in finance for a long time, notably in the areas of market simulation, risk measurement, and financial asset pricing. In this paper, we propose copula entropy models with two and three variables to measure dependence in stock markets, which extend the copula theory and are based on Jaynes’s information criterion. Both of them are usually applied under the non-Gaussian distribution assumption. Comparing with the linear correlation coefficient and the mutual information, the strengths and advantages of the copula entropy approach are revealed and confirmed. We also propose an algorithm for the copula entropy approach to obtain the numerical results. With the experimental data analysis at the country level and the economic circle theory in international economy, the validity of the proposed approach is approved; evidently, it captures the non-linear correlation, multi-dimensional correlation, and correlation comparisons without common variables. We would like to make it clear that correlation illustrates dependence, but dependence is not synonymous with correlation. Copulas can capture some special types of dependence, such as tail dependence and asymmetric dependence, which other conventional probability distributions, such as the normal p.d.f. and the Student’s t p.d.f., cannot.     

Measuring monotony in two-dimensional samples

This note introduces a monotony coefficient as a new measure of the monotone dependence in a two-dimensional sample. Some properties of this measure are derived. In particular, it is shown that the absolute value of the monotony coefficient for a two-dimensional sample is between |r| and 1, where r is the Pearson's correlation coefficient for the sample; that the monotony coefficient equals 1 for any monotone increasing sample and equals ?1 for any monotone decreasing sample. This article contains a few examples demonstrating that the monotony coefficient is a more accurate measure of the degree of monotone dependence for a non-linear relationship than the Pearson's, Spearman's and Kendall's correlation coefficients. The monotony coefficient is a tool that can be applied to samples in order to find dependencies between random variables; it is especially useful in finding couples of dependent variables in a big dataset of many variables. Undergraduate students in mathematics and science would benefit from learning and applying this measure of monotone dependence.     

A tail dependence-based dissimilarity measure for financial time series clustering

In this paper we propose a clustering procedure aimed at grouping time series with an association between extremely low values, measured by the lower tail dependence coefficient. Firstly, we estimate the coefficient using an Archimedean copula function. Then, we propose a dissimilarity measure based on tail dependence coefficients and a two-step procedure to be used with clustering algorithms which require that the objects we want to cluster have a geometric interpretation. We show how the results of the clustering applied to financial returns could be used to construct defensive portfolios reducing the effect of a simultaneous financial crisis.     

The weak tail dependence coefficient of the elliptical generalized hyperbolic distribution

The strong and the weak tail dependence coefficients are measures that quantify the probability of conjoint extreme events of two random variables. Whereas formulas for both tail dependence coefficients exist for the Gaussian and Student t distribution, only the strong tail dependence coefficient is known for their super-model, the elliptical generalized hyperbolic distribution, which is extremely popular in finance (see Schmidt 2003). In this work we derive a simple expression for the corresponding weak tail dependence coefficient using the mixture representation of the elliptical generalized hyperbolic distribution.     

Tail Risk of Multivariate Regular Variation

Tail risk refers to the risk associated with extreme values and is often affected by extremal dependence among multivariate extremes. Multivariate tail risk, as measured by a coherent risk measure of tail conditional expectation, is analyzed for multivariate regularly varying distributions. Asymptotic expressions for tail risk are established in terms of the intensity measure that characterizes multivariate regular variation. Tractable bounds for tail risk are derived in terms of the tail dependence function that describes extremal dependence. Various examples involving Archimedean copulas are presented to illustrate the results and quality of the bounds.