Copula函数的选择：方法与应用

针对目前Copula函数在实际应用中的选择问题,本文通过非参数法得到了它们的分布函数图及其经验分布图并进行了比较,然后利用一种解析法对其进一步的选择,并通过Q-Q图比较了各种模型的拟合程度,最后进行了拟合优度检验,得到了最优的Copula。最后对国内的上证A股指数和上证B股指数进行了实证分析,结果体现了该方法的有效性。     

基于GARCH-GH模型的上证50ETF期权定价研究

上证50ETF期权是中国推出的首支股票期权.为描述上证50ETF收益率偏态、尖峰、时变波动率等特征,结合GARCH模型和广义双曲(Generalized Hyperbolic,GH)分布两方面的优势,建立GARCH-GH模型为上证50ETF期权定价.在等价鞅测度下,利用蒙特卡罗方法估计上证50ETF欧式认购期权价格.实证表明,相比较Black-Scholes模型和GARCH-Gaussian模型,GARCH-GH模型得到的结果更接近于上证50ETF期权的实际价格,其定价误差最小.     

Pareto分布中门槛值的确定及其在股票市场中的应用

本文根据Pareto分布与两参数指数分布之间的相互关系,利用两参数指数分布的拟合优度检验统计量给出了确定Pareto分布的门槛值的一种方法。利用道琼斯指数和上证综合指数的收益率序列说明所给方法,结果表明所给方法优于现有方法。     

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。     

金融时变高阶矩建模及其风险测度研究:基于收益率分解的方法

本文基于收益率分解方法,将收益率表示成符号部分和绝对值部分的乘积形式,通过对符号部分、绝对值部分以及这两部分间的相关性分别进行时变性设定,构建了动态收益率分解(DRD)模型来刻画收益率的高阶矩动态特征。该模型能灵活地设置条件偏度和条件峰度的时变演化方式,还能通过对符号部分和绝对值部分间相关性的时变Copula设定来刻画收益率变动的非线性特征,因而使得该模型对收益率的预测具有优势。本文还利用上证综合指数和深证成份指数的收益率数据对DRD模型进行了实证研究,结果表明:两种股指收益率序列均表现出了显著的高阶矩动态特征,条件偏度和条件峰度存在一定程度的波动聚集特征。相较于其他时变高阶矩模型,DRD模型不仅具有更好的样本内模型拟合效果,而且在样本外的风险价值预测和经济价值评价等方面均表现出一定的优越性。     

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.     

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模型的沪深股市日收益率的相关性研究

由于沪深股市收益率具有非线性的特征,本文利用Copula函数从定量的角度刻画了上证综指和深证成指的日收益率序列的相关关系,研究表明,沪深股市日收益率序列呈现出很高的相关性,当沪深两市出现大幅震荡时,两市收益率的协同作用将大幅增强,Gaussian Copula函数更好的刻画了沪深股市收益率之间的秩相关性,Gumbel Copula函数在更好的刻画了两收益率序列的上尾相关性,而Clayton Copula函数在分析两序列的下尾相关性时较为出色,在平方欧氏距离标准下,t-Copula较好的拟合了沪深股市的日收益率序列。     

Copula函数在金融市场中的应用

本文旨在通过构造Copula模型,研究股市大盘和房地产(万科)股票之间的相关性与极值情况下的尾部相关性.在边缘分布的求取上,选用非参数核密度法分别估算出股市大盘和房地产股票的边缘分布函数值;在Copula函数的选择上,为选出最优Copula模型,选用多种方法结合包括二元分布直方图法、Q-Q图法、平方欧氏距离法;在Copula函数的参数估计上,采用惯用的极大似然估计法(MLE).其中,Q-Q图法首次应用在检验无分布函数的数据上.分析结果展现出二元t-Copula模型相对其他Copula模型可以更佳地拟合出这两支股票的联合分布;大盘股票与万科股票趋于较强的正向相关性;而极值情况下的尾部相关性相比一般时刻的正向相关性有所降低.     

沪深股市收益率的尾部相关函数

尾部相关性是相关性分析中重要的一类,利用度量尾部相关性的指标χ,χ-以及尾部相关函数ρ(θ)来分析尾部相关性,并给出ρ(θ)的一种非参数估计方法.通过这两种方法研究上证综合指数和深证成分指数日收盘指数对数收益率在损失情况下的尾部相关性,结果表明两市指数日对数收益率具有很强的尾部相关性.     

Modelling dependence structure with Archimedean copulas and applications to the iTraxx CDS index

In this paper we model the dependence structure between credit default swap (CDS) and jump risk using Archimedean copulas. The paper models and estimates the different relationships that can exist in different ranges of behaviour. It studies the bivariate distributions of CDS index spreads and the kurtosis of equity return distribution. To take into account nonlinear relationships and different structures of dependency, we employ three Archimedean copula functions: Gumbel, Clayton, and Frank. We adopt nonparametric estimation of copula parameters and we find an extreme co-movement of CDS and stock market conditions. In addition, tail dependence indicates the extreme co-movements and the potential for a simultaneous large loss in stock markets and a significant default risk. Ignoring the tail dependence would lead to underestimation of the default risk premium.     

基于Copula函数的股指尾部相关性研究——以道琼斯工业指数与恒生指数为例

鉴于两步参数估计法在应用中存在误差大、计算复杂等缺陷,采用基于经验分布的半参数估计与非参数估计法确定相应边缘分布与Copula参数,对突发事件下的道琼斯工业指数与恒生指数之间的尾部相关性进行量化.研究发现ClaytonCopula,Gumbel Copula能够较好地刻画股指收益率序列间的尾部相关关系;道指与恒生指数存在着正的尾部相关且这种相关是非对称性的;在各个置信水平上,下尾损失均较上尾收益高,且下尾相关系数的增长幅度远大于上尾相关系数的增长幅度;极端事件造成的道指收益的剧烈下跌引发了恒生指数收益更强烈的相关反应,其造成的影响远超过两个市场同时上涨时的作用.     

Dependence structure between LIBOR rates by copula method

This paper discusses the correlation structure between London Interbank Offered Rates (LIBOR) by using the copula function. We start from one simplified model of A. Brace, D. Gatarek, and M. Musiela (1997) and find out that the copula function between two LIBOR rates can be expressed as a sum of an infinite series, where the main term is a distribution function with Gaussian copula. Partial differential equation method is used for deriving the copula expansion. Numerical results show that the copula of the LIBOR rates and Gaussian copula are very close in the central region and differ in the tail, and the Gaussian copula approximation to the copula function between the LIBOR rates provides satisfying results in the normal situation.     

Tail negative dependence and its applications for aggregate loss modeling

Tail order of copulas can be used to describe the strength of dependence in the tails of a joint distribution. When the value of tail order is larger than the dimension, it may lead to tail negative dependence. First, we prove results on conditions that lead to tail negative dependence for Archimedean copulas. Using the conditions, we construct new parametric copula families that possess upper tail negative dependence. Among them, a copula based on a scale mixture with a generalized gamma random variable (GGS copula) is useful for modeling asymmetric tail negative dependence. We propose mixed copula regression based on the GGS copula for aggregate loss modeling of a medical expenditure panel survey dataset. For this dataset, we find that there exists upper tail negative dependence between loss frequency and loss severity, and the introduction of tail negative dependence structures significantly improves the aggregate loss modeling.     

房地产产业链相依结构演化及其危机传染效应研究

以钢铁、有色金属、家用电器、房地产、建筑材料、建筑装饰、银行、非银金融和机械设备九大申万一级行业指数所代表的房地产产业链为研究对象,通过采用R-Vine Copula方法来刻画房地产产业链上行业间相依结构及其在2008年金融危机冲击下的结构演化特征.研究结果表明:房地产产业链上各行业间普遍存在对称、厚尾的相依结构,行业间相依性水平较高;机械设备业在整个房地产产业链上起到了枢纽中心的连接作用;金融危机的发生增强了房地产产业链的总体相依性水平,危机传染效应显著;与CVine Copula和D-Vine Copula方法相比,R-Vine Copula更适合来刻画我国房地产产业链的相依结构特征.     

基于截断tau的copula模型选择及应用

本文引进了截断tau,计论了它与生存阿基米德Copula之间的关系,并在此基础上提出一种新的选择Copula模型的方法,实例分析表明,这种构建Copula模型的方法较好反映了数据内在的信息,客观描述金融变量的相关性,便于尾部相关性分析,为金融市场相关性分析提供了一种新途径.     

A generalized beta copula with applications in modeling multivariate long-tailed data

This work proposes a new copula class that we call the MGB2 copula. The new copula originates from extracting the dependence function of the multivariate GB2 distribution (MGB2) whose marginals follow the univariate generalized beta distribution of the second kind (GB2). The MGB2 copula can capture non-elliptical and asymmetric dependencies among marginal coordinates and provides a simple formulation for multi-dimensional applications. This new class features positive tail dependence in the upper tail and tail independence in the lower tail. Furthermore, it includes some well-known copula classes, such as the Gaussian copula, as special or limiting cases.To illustrate the usefulness of the MGB2 copula, we build a trivariate MGB2 copula model of bodily injury liability closed claims. Extended GB2 distributions are chosen to accommodate the right-skewness and the long-tailedness of the outcome variables. For the regression component, location parameters with continuous predictors are introduced using a nonlinear additive function. For comparison purposes, we also consider the Gumbel and t copulas, alternatives that capture the upper tail dependence. The paper introduces a conditional plot graphical tool for assessing the validation of the MGB2 copula. Quantitative and graphical assessment of the goodness of fit demonstrate the advantages of the MGB2 copula over the other copulas.     

天然气期货和现货价格间的相关性研究

基于天然气期货价格与现货价格序列间具有强非线性特征,本文将GARCH模型和Copula函数思想进行结合,同时考虑了天然气期货和现货价格间的时变相关结构,构建了时变Copula(GARCH-Normal、GARCH-GED和GARCH-t)模型,利用美国纽约商品交易所(NYMEX)Henry Hub交易中心天然气期货价格和现货价格数据进行实证研究。实证结果表明:GARCH-GED模型能够准确地拟合天然气期货与现货价格时间序列;时变SJC-Copula函数能够更好的描述天然气期货价格与现货价格间的相关性;天然气期货与现货价格间的相关性不是对称的,上尾的相关性小于下尾相的相关性。     

Modeling multi-country mortality dependence and its application in pricing survivor index swaps—A dynamic copula approach

This paper introduces mortality dependence in multi-country mortality modeling using a dynamic copula approach. Specifically, we use time-varying copula models to capture the mortality dependence structure across countries, examining both symmetric and asymmetric dependence structures. In addition, to capture the phenomenon of a heavy tail for the multi-country mortality index, we consider not only the setting of Gaussian innovations but also non-Gaussian innovations under the Lee–Carter framework model. As tests of the goodness of fit of different dynamic copula models, the pattern of mortality dependence, and the distribution of the innovations, we used empirical mortality data from Finland, France, the Netherlands, and Sweden. To understand the effect of mortality dependence on longevity derivatives, we also built a valuation framework for pricing a survivor index swap, then investigated the fair swap rates of a survivor swap numerically. We demonstrate that failing to consider the dynamic copula mortality model and non-Gaussian innovations would lead to serious underestimations of the swap rates and loss reserves.     

相关系数与相关性度量

研究了度量相关性的两个主要工具:线性相关系数和尾部相关系数.线性相关系数反映了变量间的线性相关性,这对于一般的椭圆型分布是合适的.但如果随机变量具有不对称的尾部变化特征时,要用尾部相关系数描述它们之间的相关性.通过相关函数C opu la,对沪深股市的尾部相关系数进行了定量分析.结果表明:沪深股市具有较强的相关性.