基于多维Gumbel Copula函数的投资组合VaR分析

基于目前国内有关Copula函数的实证研究主要是研究二种资产的相关性为主,文章根据Copula函数在构建反映随机变量实际分布与相关性的联合分布函数上具有的优势,首先利用GJR模型构建资产的边缘分布,接着利用多元阿基米德Copula函数族中的Gumbel Copula函数构建了反映多个资产收益实际分布和相关性的联合分布函数,并使用蒙特卡罗模拟技术,分析在不同置信度下的投资组合的最小风险价值(VaR)及其资产组成,实证说明根据文章提出的模型度量资产的风险,可以使投资者选择的资产更加稳健,同时也有利于投资者对投资组合整体风险进行分散和监管。     

基于Copula的VsR度量与事后检验

估计VaR的传统方法有三种:协方差矩阵法、历史模拟法和蒙特仁洛模拟法。通常,文献中认为刚蒙特卡洛模拟法度量VaR有很多方面的优点。但是,本文通过实证检验发现,使用传统蒙特卡洛模拟法估计的VaR偏小,事后检验效果很不理想。本文引入Copula函数来改进传统的蒙特卡洛模拟法。Copula函数能将单个边际分布和多元联合分布联系起来,能处理非正态的边际分布,并且它度量的相关性不再局限于线性相关性。实证检验表明,基于Copula的蒙特卡罗模拟法可以更加准确地度量资产组合的VaR。     

藤Copula模型与多资产投资组合VaR预测

投资组合风险管理往往涉及多个资产,在传统的二元Copula函数面临"维度诅咒"问题及多元Copula函数刻画多变量联合分布时其精确性和灵活性存在各种局限性的情况下,引入藤Copula刻画多个资产收益的联合分布,基于不同的Pair-Copula类别构建藤Copula,运用蒙特卡罗模拟方法计算多资产投资组合的VaR,通过Kupiec和Christoffersen返回检验方法测试藤Copula模型的VaR预测效果,并与传统方差-协方差风险管理方法做比较。实证分析表明,传统的方差-协方差风险管理方法和基于正态Pair-Copula作为藤Copula构建模块的方法不能通过多资产投资组合的VaR预测返回检验;而基于student-t Copula、Clayton Copula具有尾部分布特征的Copula作为构建模块的藤Copula模型能够有效地用于多资产投资组合VaR预测,从而更好的用于指导实践。     

基于SVt-EVT-Vine Copula的投资组合VaR研究

针对现有风险度量模型不能准确的模拟高维金融资产收益率风险,以上证指数、沪深300指数和股指期货指数为例,首先利用SVt和EVT对各序列的边缘分布进行建模,然后采用Vine Copula方法分析多序列之间的秩相关关系和极大似然值估计法估计参数,得到RVine,CVine和DVine三种不同树结构的分解模型,通过Monte Carlo模拟法计算出在同一边缘分布不同Vine Copula方法下和在不同边缘分布同一Vine Copula方法下单资产和投资组合的金融风险VaR.经实证检验并分析对比,VaR和返回式检验均表明SVt和EVT相结合对边缘分布有较好的拟合效果,再运用RVine描述资产间的相依结构在度量投资组合金融风险方面更准确合理.     

基于Clayton Copula-GARCH模型投资组合VaR的度量

运用Copula方法研究了含股指期货的投资组合的风险度量问题.首先采用不同的GARCH模型对单个资产收益率建模,然后选择Clayton Copula函数来描述投资组合各资产之间的相关结构,建立联合分布模型,进而采用Monte Carlo方法模拟产生各资产的收益率序列,计算出投资组合的VaR.Kupiec检验表明,ClaytonCopula-GARCH模型在投资组合风险度量上具有较高的准确性.     

基于TGARCH-t的混合Copula投资组合风险测度研究

在分析了现有Copula函数在测度投资组合风险不足的情况下,首先充分考虑资产波动的时变性、杠杆效应等特征,选择了TGARCH-t模型进行边缘分布建模.接着引入混合Copula模型来描述投资组合的复杂相关结构,同时利用构造的主对角线距离统计量等方法验证了混合Copula模型的优势.最后通过VaR的蒙特卡洛模拟结果看到,这种方法能更为精确的测度投资组合风险值.     

股票市场组合的市场风险度量研究——基于相关性模型

利用Copula的特点,灵活选择边缘分布模型、Copula函数和时变参数演化方程,构建16个相关性模型.在此基础上,通过蒙特卡罗模拟,采用VaR和ES度量资产组合的市场风险,并通过回测检验比较不同模型的风险度量效果.以沪深300指数和恒生指数为样本构建投资组合进行实证研究,结果表明,边缘分布模型、Copula时变参数演化方程和Copula函数的选择会影响风险度量的精度.在构建的16个相关性模型中,边缘分布为MSM-EVT,时变参数演化方程为GAS模型,Copula函数为Rotated Gumbel Copula的MSM-EVT-R-GAS模型风险度量效果最好.     

基于极值统计和高维动态C藤Copula的股市行业集成风险计算

股市诸多行业风险之间存在着波动相依性,集成计量多维风险对投资决策意义重大。藤Copula是Copula函数高维化拓展的一个方向,其动态化是新的研究前沿。将极值理论的GPD模型和高维动态C藤Copula方法结合起来研究沪深300指数中地产、基建、银行和运输四个行业风险,能够有效描述尾部极值形态,突出关键变量的作用。再运用动态Pair-Copula分解,刻画高维行业风险变量间的动态关系,以仿真出动态集成风险变量VaR序列。VaR计算结果通过了回溯检验和稳定性测试,表明高维动态C藤Copula模型可以作为风险集成计量的一种新的有效方法。     

沪深股市的相关结构分析与投资组合风险度量——基于ARFIMA-GARCH-Copula模型

金融资产收益率不仅具有尖峰厚尾性、异方差性,还具有长记忆性。基于此,本文建立ARFIMA-GARCH-Copula模型来研究沪深股市的相关结构和等权重投资组合风险值VaR,利用上证指数和深成指数收益率的组合来进行实证研究。首先采用经典R/S分析法检验各个资产收益率的长记忆性,经过分数阶差分后选用GARCH模型建模得到边缘分布。然后选择Copula函数来刻画两资产之间的相关结构,建立联合分布模型。进而采用Monte Carlo方法模拟产生各资产的收益率序列,计算出投资组合的风险值VaR。实证研究表明:沪深股市具有长记忆性,且两者具有对称的尾部相关性;Kupiec检验说明ARFIMA-GARCH-Copula模型较之于GARCH-Copula模型能更准确地度量投资组合风险。     

基于半参数多元Copula-GARCH模型的开放式基金投资组合风险分析

利用Copula技术对我国开放式基金市场的投资组合进行了风险分析。为克服传统Copula模型对金融尾部数据刻画能力的不足,建立了半参数的多元Copula-GARCH模型,灵活地对各支基金的边缘分布进行拟合,刻画了开放式基金投资组合的相依结构。并利用基于Copula技术的蒙特卡洛模拟,对投资组合进行了VaR分析,结果证实了所建立模型的可行性和有效性。     

From extended regular variation to regular variation with application in extreme value statistics

This paper aims to provide a study of a variety of concepts involving power behavior of eventually positive functions which, falling under the umbrella of the Theory of Regular Variation and its second order refinements, are prone to application in Extreme Value Theory. To this extent, some well-known properties shall be resumed, others will be designed with the ultimate purpose of establishing a relation between regular variation and extended regular variation of second order. As a by-product, new ways of looking at some common estimators for the extreme value index, in particular the maximum likelihood estimator, will be unveiled.     

The expected payoff to Internet auctions

In an Internet auction, the expected payoff acts as a benchmark of the reasonableness of the price that is paid for the purchased item. Since the number of potential bidders is not observable, the expected payoff is difficult to estimate accurately. We approach this problem by considering the bids as a record and 2-record sequence of the potential bidder’s valuation and using the Extreme Value Theory models to model the tail distribution of the bidder’s valuation and study the expected payoff. Along the discussions for three different cases regarding the extreme value index γ, we show that the observed payoff does not act as an accurate estimation of the expected payoff in all the cases except a subclass of the case γ = 0. Within this subclass and under a second order condition, the observed payoff consistently converges to the expected payoff and the corresponding asymptotic normality holds.      

基于Bayes估计的金融风险值——VaR计算

初步研究了用Bayes估计计算金融风险值VaR,同时阐明了运用极值理论方法在Bayes估计下的金融风险值计算。并且借助统计计算方法——MCMC算法来求解参数的Bayes估计,有效的将Bayes思想融入到了VaR的计算中。用Bayes估计计算金融风险值VsR,可以帮助投资者将观测数据和自己所掌握的经验信息对VaR模型进行调整,使得vsR模型能够更准确地反映出金融市场的风险状况,据此做出更加正确的投资决策。     

Hitting time statistics and extreme value theory

We consider discrete time dynamical systems and show the link between Hitting Time Statistics (the distribution of the first time points land in asymptotically small sets) and Extreme Value Theory (distribution properties of the partial maximum of stochastic processes). This relation allows to study Hitting Time Statistics with tools from Extreme Value Theory, and vice versa. We apply these results to non-uniformly hyperbolic systems and prove that a multimodal map with an absolutely continuous invariant measure must satisfy the classical extreme value laws (with no extra condition on the speed of mixing, for example). We also give applications of our theory to higher dimensional examples, for which we also obtain classical extreme value laws and exponential hitting time statistics (for balls). We extend these ideas to the subsequent returns to asymptotically small sets, linking the Poisson statistics of both processes.     

基于藤结构 Copula 模型的中国股市风格资产相依结构研究

首先采用AR（1）-GJR（1,1）-SkT（73,A）模型来刻画中国股市风格资产（大盘成长、大盘价值、中盘成长、中盘价值、小盘成长、小盘价值）的边缘分布,接着结合各边缘分布的残差,引入C—VineCop—ula和r）IVineCopula模型来描述这六种风格资产之间的相依结构,然后对基于CVineCopula和I）IVineCopula模型的拟合效果进行综合比较．研究结果表明：中国股市各风格资产之间的相依性存在结构性差异,最适合用I）IVineCopula模型来刻画各风格资产之间的相依结构．同类型的风格资产之间的相依程度比不同类型风格资产之间的相依程度要高;在同一类型的风格资产中,资产规模差距越大的风格资产之间的相依系数就越小．无条件的风格资产收益系列之间的相关性要显著大于有条件的风格资产收益系列之间的相关性;最后根据研究结论提出了降低风格资产组合风险的资产配置建议．     

Copula convergence theorems for tail events

Tail dependence is studied from a distributional point of view by means of appropriate copulae. We derive similar results to the famous Pickands–Balkema–de Haan Theorem of Extreme Value Theory. Under regularity conditions, it is shown that the Clayton copula plays among the family of archimedean copulae the role of the generalized Pareto distribution. The practical usefulness of the results is illustrated in the analysis of stock market data.     

Dependence structure of risk factors and diversification effects

In this paper, we study the aggregated risk from dependent risk factors under the multivariate Extreme Value Theory (EVT) framework. We consider the heavy-tailedness of the risk factors as well as the non-parametric tail dependence structure. This allows a large range of models on the dependence. We assess the Value-at-Risk of a diversified portfolio constructed from dependent risk factors. Moreover, we examine the diversification effects under this setup.     

Asymptotics for risk capital allocations based on Conditional Tail Expectation

An investigation of the limiting behavior of a risk capital allocation rule based on the Conditional Tail Expectation (CTE) risk measure is carried out. More specifically, with the help of general notions of Extreme Value Theory (EVT), the aforementioned risk capital allocation is shown to be asymptotically proportional to the corresponding Value-at-Risk (VaR) risk measure. The existing methodology acquired for VaR can therefore be applied to a somewhat less well-studied CTE. In the context of interest, the EVT approach is seemingly well-motivated by modern regulations, which openly strive for the excessive prudence in determining risk capitals.     

The long‐term extreme price risk measure of portfolio in inventory financing: An application to dynamic impawn rate interval

Different from the short‐term risk measure for traditional financial assets (stocks, bonds, etc.), the key to illiquid inventory portfolio traded in the over‐the‐counter markets is to estimate the long‐term extreme price risk with time varying volatility. In this article, a new long‐term extreme price risk (value at risk and conditional value at risk) measure method for inventory portfolio and an application to dynamic impawn rate interval are proposed. To realize this, we first establish AutoRegressive Moving Average‐Exponential Generalized Autoregressive Conditional Heteroskedasticity‐Extreme Value Theory model and multivariatet‐Copula to depict the autocorrelation, fat tails, and volatility clustering of returns of inventories and the nonlinear dependence structure of inventories. Furthermore, we obtain the long‐term extreme price risk with time varying volatility via Monte Carlo simulation instead of square‐root‐of time rule. The results show that, first, benefits from risk diversification is significant; second, long‐term extreme price risk measure of inventory portfolio via Monte Carlo method outperforms the square‐root‐of time rule; the last is that the dynamic rate interval based on the long‐term price risk is superior to the crude rules of thumb in terms of reducing efficiency loss and improving risk coverage. In summary, this article provides a new quantitative framework for managing the risk of portfolio in inventory financing practice for banks constrained by risk limitation. © 2014 Wiley Periodicals, Inc. Complexity 20: 17–34, 2015