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。     

尾部极值分布下的系统性金融风险度量及影响因素分析

本文将极值理论应用到系统性金融风险度量上,在尾部极值分布的假设下应用极端的分位数回归度量尾部的风险并研究风险变化和风险的相依性,本文度量了单一机构的系统性风险贡献并识别出我国的系统重要性金融机构。另外,本文还使用面板回归分析了金融机构系统性风险贡献的影响因素。本文得到的主要结论有:在险价值和系统性风险贡献在评价金融机构风险上的差异很大;银行类金融机构的系统性风险贡献普遍较高;金融机构的规模和杠杆率两个特征变量对系统性风险贡献的影响最显著。政策建议方面本文认为要综合考虑金融机构规模、杠杆率、股票市场贝塔值等多个特征变量,对金融机构尤其是银行类金融机构进行资本监管和约束。     

运用Student T-Copula的极值理论度量我国商业银行的操作风险

银行操作风险损失数据具有厚尾性,同时不同损失事件之间具有相关性.依据巴塞尔委员会对操作风险损失类型的界定,利用从公开渠道收集的我国商业银行内部欺诈和外部欺诈损失数据.运用基于Studentt-Copula的极值理论研究我国商业银行面临的操作风险,得出极值理论的POT模型能够有效地捕捉损失厚尾性,计算出的VaR比较准确,只是不同的损失数据对阈值的选取存在一定差异.进一步研究表明采用Studentt-Copula刻画两种损失事件之间的相关性,能够有效地降低VaR,降幅甚至高达40%以上.既可以为银行节省大量经济资本,有利于日常经营,又可以准确计提经济资本,有利于监管当局的监管.     

基于g-h分布的操作风险损失强度分布拟合及风险度量

操作风险损失强度分布呈现的"右偏性、厚尾性"特点,使操作风险损失强度的拟合面临着许多困难。为了解决传统损失分布难以拟合损失分布尾部的问题,同时又为了克服极值理论的弊端,将四参数的g-h分布用于操作风险损失强度拟合中,设计当损失强度分布为g-h分布时使用Monte Caro模拟的基本步骤。并以我国的517个风险损失数据为基础,以实证分析的形式验证所提出的方法,将拟合结果与尾部风险及其他4种常用分布进行比较。实证结果显示,在损失强度的拟合中,g-h分布能较好的捕获操作风险损失分布的"厚尾"特性,对操作风险损失分布的拟合效果最好,尾部风险计算较为合理。     

极值copula的统计推断及实证研究

为了分析由极端事件所引起的巨额损失变量之间的相依关系,本文引入了比一般copula函数更有效的极值copula和上尾copula。我们介绍copula的对角截面以确定上尾相依系数。基于极大似然法,讨论了关于这些copula函数类的半参数估计方法。通过构建Cramer-Von Mises统计量对copula的拟合优度进行假设检验。在实证分析部分,我们通过具体的实例来说明,在应用研究中该如何选取最优的copula以描述变量之间的相关性。     

基于分段损失分布法和Copula的银行操作风险集成度量

多个风险单元的集成度量是银行操作风险管理的关键步骤之一。立足于操作风险的“厚尾”、“截断”性,从分段损失分布法的视角出发,探讨操作风险集成度量的模式和数值方法。首先,引入两阶段损失分布法来拟合单个风险单元边际损失分布,用双截尾分布代替传统的完整分布来刻画“高频低损”损失数据的双截断特性,利用POT模型捕获“低频高损”事件的厚尾特性。再次,基于分段建模思路,对传统度量过程中边际分布为单一、完整分布的Copula模型进行了扩展,研究边际分布为分段分布、截尾分布条件下使用Copula函数集成度量操作风险的框架和步骤,并设计了Monte Carlo模拟算法。最后,以实证分析的形式验证所构建模型。通过对中国商业银行416个操作风险损失数据的实证分析,结果表明分段分布、截尾分布能对单个风险单元边际分布有更好的拟合效果,能减小由于分布选择不当而引发的模型风险。分段度量视角下Copula函数的引入能灵活处理多个操作风险单元间的相依结构,使风险度量结果更为合理。     

国际碳排放权市场动态相依性分析及风险测度:基于Copula-GARCH模型

选取2009年3月13日-2010年8月4日的CER和EUA交易价格数据,借用CopulaGARCH模型,文章对欧洲气候交易所EUA和CER现货市场与期货市场之间的动态相依性进行了分析。分别选取Student-t DCC、Student-t TVC、Gaussian DCC、G3,ussian TVC和SJCPatton五种动态Copula函数来捕捉市场之间的动态相依性结构,研究表明Student-t DCC动态Copula函数能够更好地描述EUA和CER现货市场与期货市场之间的动态相依性。此外,EUA和CER各市场之间存在较强的对称尾部相依性,而非对称尾部相依性的证据尚不十分充足.进一步地,文章基于动态相依性分析运用Monte Carlo方法模拟国际碳排放权市场投资组合的风险VaR。     

风格股票指数的随机动态相依性研究

准确刻画风格股票的联合分布,特别是它们之间的相依性,对基金公司等机构投资者进行资产配置和风险管理都有重要意义。根据已有文献,风格股票指数的相依性与流动性等来自市场的随机变量有关,那么这种动态相依性也可能是随机的。因此,本文在研究我国风格股指数相依性时,考虑了随机形式的动态相依性。文章在Hafner和Manner(2012)随机Copula模型中加入了换手率解释变量,实证分析我国风格股票指数间的相依结构,并从风险管理的角度讨论了随机相依性的经济意义。研究发现,大盘股和小盘股、成长型和价值型股票间的尾部相依性都表现出随机动态特征。考虑随机相依性的投资策略所得组合风险比Patton(2006)模型对应的投资策略低约0.30%-1.20%。对每天、每周或每月调整投资比例的中短期投资者而言,建议考虑风格指数的随机动态相依性。而且,短期投资者在大、小盘股票上投资时,还可以使用换手率信息预测未来1天两风格指数的相依性,以进一步降低组合风险。     

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-EVT模型的干旱灾害风险评估

干旱历时和干旱强度是影响干旱灾害风险的主要因素。根据干旱灾害发生的极端过程特点,用极值理论刻画干旱灾害风险两个特征变量的边缘分布,用Archimedes Copula函数捕捉旱灾风险两个特征变量之间的极值相依结构,本文构建的基于Copula-EVT的旱灾风险评估模型较好地反映了旱灾形成的极端过程和影响因子。实证分析以淮河流域蚌埠站为例,证实了ClaytonCopula-EVT模型能较好地拟合蚌埠站干旱灾害风险的历史经验分布,计算得出:蚌埠站干旱历时大于5个月,干旱强度超过7.45的极端干旱灾害风险概率为3%,重现期T_∩(t,d)为32.4年,对干旱历时和干旱强度的条件重现期研究得出干旱强度的取值对干旱灾害风险重现期的影响较大。     

Orthant tail dependence of multivariate extreme value distributions

The orthant tail dependence describes the relative deviation of upper- (or lower-) orthant tail probabilities of a random vector from similar orthant tail probabilities of a subset of its components, and can be used in the study of dependence among extreme values. Using the conditional approach, this paper examines the extremal dependence properties of multivariate extreme value distributions and their scale mixtures, and derives the explicit expressions of orthant tail dependence parameters for these distributions. Properties of the tail dependence parameters, including their relations with other extremal dependence measures used in the literature, are discussed. Various examples involving multivariate exponential, multivariate logistic distributions and copulas of Archimedean type are presented to illustrate the results.     

系统风险不同预期下的存款保险费率测算

将影响银行资产价值的风险因素分解为系统风险因素和银行特定风险因素,进而在系统风险因素点估计和区间估计的不同预期下测算银行存款保险费率水平,得到的费率能够反映银行资产风险随经济形势波动的变化情况。通过模拟测算了我国16家上市银行2008~2016年间特定经济形势情境下的存款保险费率水平,并在极端压力下与传统Merton费率进行了比较。得到的基本结论包括:不同年度不同银行费率对系统风险因素的敏感程度不同;经济形势尾部极端分布对费率的影响具有非对称性特点,风险极高区间对费率的贡献远大于风险极低区间;与传统的Merton费率相比,系统风险特定预期下测算的费率更契合经济形势的变化,这在存款保险制度运行初期,有利于增强基金的抗压能力。     

The optimal operational risk capital requirement by applying the advanced measurement approach

The purpose of this paper is to construct a risk quantification model to achieve the accurate operational risk management and gain the satisfying estimation and control of future possible extreme losses by using capital charges to assess operational risk. The paper takes a case bank as the research object and compares the differences under various circumstances engaging the Basic Indicator Approach, the Standardized Approach, and the Advanced Measurement Approach for the operational risk capital requirement of a bank. The results indicate that it is more appropriate to adopt the Advanced Measurement Approach to estimate the operational risk capital requirement; this way can help a bank enjoy a much lessened capital charge required and subsequently its available capital increases. Hence, it allows a bank to have sufficient funds in operations and reduce the burden of capital costs. Therefore, it will bring the positive benefits to the whole banking industry when enforcing the Advanced Measurement Approach.     

Tail dependence of the Gaussian copula revisited

Tail dependence refers to clustering of extreme events. In the context of financial risk management, the clustering of high-severity risks has a devastating effect on the well-being of firms and is thus of pivotal importance in risk analysis.When it comes to quantifying the extent of tail dependence, it is generally agreed that measures of tail dependence must be independent of the marginal distributions of the risks but rather solely copula-dependent. Indeed, all classical measures of tail dependence are such, but they investigate the amount of tail dependence along the main diagonal of copulas, which has often little in common with the concentration of extremes in the copulas’ domain of definition.In this paper we urge that the classical measures of tail dependence may underestimate the level of tail dependence in copulas. For the Gaussian copula, however, we prove that the classical measures are maximal. The implication of the result is two-fold: On the one hand, it means that in the Gaussian case, the (weak) measures of tail dependence that have been reported and used are of utmost prudence, which must be a reassuring news for practitioners. On the other hand, it further encourages substitution of the Gaussian copula with other copulas that are more tail dependent.     

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.     

Tail dependence functions and vine copulas

Tail dependence and conditional tail dependence functions describe, respectively, the tail probabilities and conditional tail probabilities of a copula at various relative scales. The properties as well as the interplay of these two functions are established based upon their homogeneous structures. The extremal dependence of a copula, as described by its extreme value copulas, is shown to be completely determined by its tail dependence functions. For a vine copula built from a set of bivariate copulas, its tail dependence function can be expressed recursively by the tail dependence and conditional tail dependence functions of lower-dimensional margins. The effect of tail dependence of bivariate linking copulas on that of a vine copula is also investigated.     

On a bivariate copula with both upper and lower full-range tail dependence

Copula functions can be useful in accounting for various dependence patterns appearing in joint tails of data. We propose a new two-parameter bivariate copula family that possesses the following features. First, both upper and lower tails are able to explain full-range tail dependence. That is, the dependence in each tail can range among quadrant tail independence, intermediate tail dependence, and usual tail dependence. Second, it can capture upper and lower tail dependence patterns that are either the same or different. We first prove the full-range tail dependence property, and then we obtain the corresponding extreme value copula. There are two applications based on the proposed copula. The first one is modeling pairwise dependence between financial markets. The second one is modeling dynamic tail dependence patterns that appear in upper and lower tails of a loss-and-expense data.     

质押贷款下的贷款价值比的研究

当零售商以仓单质押的模式向银行申请贷款时,如果零售商面临着报童问题,那么零售商的生产经营决策,就会影响到质押物的价格,从而影响到银行的利润.从企业-银行不合作博弈的角度出发,考虑质押物的处理价不高于储存费用的情况下,银行的贷款价值比的确定问题.研究发现,当银行付予物流企业的监管费用高于某一数值时,银行的贷款行为将使其利润为负.     

Tail subadditivity of distortion risk measures and multivariate tail distortion risk measures

In this paper, we extend the concept of tail subadditivity (Belles-Sampera et al., 2014a; Belles-Sampera et al., 2014b) for distortion risk measures and give sufficient and necessary conditions for a distortion risk measure to be tail subadditive. We also introduce the generalized GlueVaR risk measures, which can be used to approach any coherent distortion risk measure. To further illustrate the applications of the tail subadditivity, we propose multivariate tail distortion (MTD) risk measures and generalize the multivariate tail conditional expectation (MTCE) risk measure introduced by Landsman et al. (2016). The properties of multivariate tail distortion risk measures, such as positive homogeneity, translation invariance, monotonicity, and subadditivity, are discussed as well. Moreover, we discuss the applications of the multivariate tail distortion risk measures in capital allocations for a portfolio of risks and explore the impacts of the dependence between risks in a portfolio and extreme tail events of a risk portfolio in capital allocations.