APD分布、在险价值与DQ检验-VaR参数估计及回溯测试的改进研究

发布时间：2018-04-20 19:56

本文选题：APD分布 + 偏t分布　；参考：《西南财经大学》2013年硕士论文

【摘要】：将方差作为风险度量受到很多批评,首先方差无法刻画风险的非对称性,其次对于特定分布(如信用风险)其二阶矩可能不存在。自1994年,J.P.Morgen首次将基于VaR模型的RiskMetric公开,VaR已经成为金融业进行风险度量的行业标准。假定X为代表损益的随机变量,F为X的边际分布函数,VaR的数学定义可以如下：VaRα(x)=inf(x∈R,F(x)≥α) VaR在实践中获得了广泛的应用,但其理论存在一些缺陷,众所周知的一点就是VaR不是一致性风险度量,不满足次可加性的公理性条件。尽管如此,将VaR定义为一定置信水平下,资产组合在未来特定时间内的最大可能损失,其概念很容易在直觉上被监管者、管理层和市场参与者所理解；Danielesson et al.(2005)的研究认为尽管存在不少对VaR的批评,但这些问题对于VaR的实践不十分重要。目前,已有超过1000家以上的银行、非金融机构、保险公司、共同基金和其他资产管理机构宣称使用VaR来度量金融市场风险。 VaR方法的理论研究,主要集中在以下几个方面：一是如何准确的刻画损失分布的非对称和厚尾特征,以提高VaR建模的准确性；二是如何在众多计算方法中选择合适的方法,因为大量实证研究表明不同的VaR估计方法导致的风险值差异会很大；三是VaR的评价体系的建立,到目前为止没有一个统一而标准的体系,而如何正确评估模型预测质量是基于VaR方法的金融风险管理的关键；四是非椭圆分布下,VaR不满足次可加性,不是一个一致性风险度量,因此如何改进VaR模型和寻求替代方法是目前的研究热点。为此,本文总结国内外文献的基础上,对在VaR的估计和检验两个方面进行相应的研究。目前,VaR的估计存在三种方法,参数方法(如GARCH方法,RiskMtrics)、半参数方法(如极值理论、CAViaR)和非参数方法(如历史模拟法)。非参数方法与半参数方法的优点在于对真实数据的产生过程施加较少的约束和假定,但是这两种方法在计算VaR时,很难估计到VaR的渐进协方差矩阵。参数估计方法对损失分布施加了很强的约束,但其易于估计并容易进行后续检验,但参数方法估计的VaR的准确性很大程度上决定于风险因子损失分布的正确假定。实证研究表明,金融资产损失分布的尾部并非如同正态分布那样呈现指数平方衰减,更加平缓,尾部较正态分布更厚。损失分布的另一个重要特征是非对称性,即存在杠杆效应,这是因为投资者一般更关注下方风险,即损失边。Komunjer(2007)认为选择的分布族必须能够包含最普遍的基准分布：如正态分布、拉普拉斯分布,同时能够模拟真实市场数据的各种特征：如厚尾和非对称性,具有闭合的密度函数形式,以利于估计和检验。稳定分布(Stable distribution)、Person分布族、Tukey-λ,分布族,能够拟合很大范围的偏度和峰度,对金融资产损失分布厚尾和非对称性的特征具有很好的描述能力,但是这些分布的密度函数不是封闭形式,因此不能通过最大似然估计方法来估计。偏t分布为t分布的扩展,亦可用于拟合损失分布的这两种特征,其在风险度量建模上也有相应应用,但偏t分布的密度函数不是对数凹的,若t分布的自由度小于四,t分布不存在有限的四阶距。Gram-Charlier分布的缺点在于必须对偏度和峰度进行某些限定,以满足密度函数非负的条件,其最大似然估计明显受到初值选择的影响。因此,本文用Komunjer(2007)提出的非对称幂分布(APD)来拟合损失分布,以APD-VaR参数方法为研究对象,以统计学和金融学为研究工具,以定量实证研究为主,结合定性分析讨论,集中深入地的研究基于APD-VaR方法的金融、风险度量模型的理论与应用。探讨了APD分布的统计特性,提出了基于标准GARCH模型的GARCH-APD-VaR参数方法,阐述了该方法的性质、特点和应用。 VaR存在多种估计方法,这意味着对同一资产或资产组合会导致不同的风险评估,实证研究表明其差异甚至会非常大。因此,必须对建立的度量模型进行验证,检验VaR模型预测质量方法有很多,本文讨论所谓的“事件概率预测法”,这种方法是在给定覆盖率下检验真实收益序列对VaR预测序列的突破过程,包括两个部分：非条件覆盖检验和独立性检验。目前在应用层面上使用较多是似然比检验,该检验假定数据满足一阶马尔科夫链假定,这种约束较强。实际运用中,数据可能并不满足这种的假定,并且该方法未考虑高阶自相关的存在和任何其他外生变量对VaR模型有效性的影响。基于此,本文引入一种较新的VaR模型验证方法——动态分位数检验(DQ Test)来作为似然比检验的补充,建立了似然比检验和动态分位数检验相结合的VaR评价体系。本文的主要研究工作及成果可归纳如下：1.第一章为本文的绪论部分,阐述本文的研究背景,并在系统分析VaR研究现状的基础上,指出VaR的研究方向,最后提出了本文要解决的问题,以及研究的意义和创新之处。2.第二章为文献综述,笔者对VaR的研究文献进行了梳理,对VaR方法的起源、发展进行了深入的讨论；对VaR估计方法和检验方法进行必要的述评,明了其适用范围和局限性等。3.第三章为风险管理的理论基础,首先阐述金融风险的概念、特点和分类,详细分析了金融市场风险管理的动因、功能和管理过程,深入讨论了金融市场风险度量方法及其历史演变,以及金融市场风险的度量框架。4.第四章研究在APD分布假设下VaR的参数估计方法,在这一部分对VaR的原理、定义和计算方法进行了介绍,提出了在偏t分布和APD分布下的动态建模方法。5.第五章主要探讨VaR的回溯测试方法,该部分对目前主流的检验方法的假设条件、特点和局限性进行了必要的分析,在这些分析的基础上提出了似然比检验和动态分位数检验(DQ检验)相结合VaR样本外评价体系。6.第六章为本文的实证部分,我们选取上证综合指数来进行计量分析,发现损失分布存在明显的厚尾和偏斜现象,同时收益序列存在一阶自相关和二阶自相关现象,这表明引入APD分布和GARCH模型的合理性；从VaR样本外评估结果看,如果基于似然比检验,在95%和99%两个置信水平下,基于APD分布的VaR都是最优模型；动态分位数检验下,虽然总体而言APD分布相对其他概率分布函数有很大优势,但与似然比检验结果比较却有很大的不同,在95%的显著性水平下仅有少量模型合格,而在99%的置信水平下任何预测间隔都没有一个模型是合格的,由于我们无法观测到真实的VaR值,因此这一结果让我们关注到选择统计检验模型的重要性。7.第七章为本文的结论部分,对本文的研究进行了总结,并对今后的研究做出了展望。本文的特色和创新之处在于：提出基于APD分布的动态VaR分析框架,应用于基于损益的APD-VaR参数模型表明APD分布能够有效的提高VaR的预测质量；提出了似然比检验和动态分位数检验相结合的风险度量回溯检验体系。笔者力图在VaR建模及VaR检验两个方面对VaR理论与应用的完善提供一些供有价值的信息。
[Abstract]:In 1994 , J . P . Morgen first published RiskMetric based on VaR model , VaR has become the industry standard of risk measure in finance industry .

VaR is widely used in practice , but its theory has some drawbacks . It is well known that VaR is not a consistent risk measure . It does not meet the public reason condition of subadditivity . However , VaR is defined as a certain confidence level , and the maximum possible loss of portfolio in future specific time is easily understood by regulators , management and market participants ;
But these problems are not critical to the practice of VaR , though there are not quite a few criticisms of VaR . More than 1,000 banks , non - financial institutions , insurance companies , mutual funds and other asset management agencies have announced the use of VaR to measure financial market risks .

The theoretical research of VaR method focuses on the following aspects : First , how to accurately depict the asymmetric and thick tail features of the loss distribution to improve the accuracy of VaR modeling ;
Second , how to select the right method in many calculation methods , because a large number of empirical studies show that different VaR estimation methods result in a great difference in risk value ;
The third is the establishment of VaR evaluation system , so far there is no unified and standard system , and how to correctly evaluate the model forecast quality is the key to the financial risk management based on VaR method ;
In non - elliptic distribution , VaR does not meet the subadditivity , is not a consistency risk measure , so how to improve VaR model and seek alternative method is the current research hotspot .

In this paper , based on the domestic and foreign literatures , this paper makes a corresponding research on the estimation and test of VaR . At present , there are three methods for estimating VaR . The method of non - parametric method and semi - parametric approach is very difficult to estimate . In this paper , the theory and application of the financial and risk measure model based on APD - VaR method are discussed and discussed in detail . The statistical characteristics of APD distribution are discussed , and the parameter method based on the standard ARCH model is put forward . The property , characteristics and application of the method are expounded .

There are a number of estimation methods for VaR , which means that the same asset or portfolio can lead to different risk assessments . The empirical research shows that the difference is even very large . Therefore , it is necessary to validate the established metric model . This method is based on the assumption that the real revenue sequence is not satisfied with this assumption . In practice , the data may not satisfy this assumption , and the method does not take into account the existence of high - order autocorrelation and any other exogenous variable to the validity of VaR model .

The main research work and achievements of this paper can be summarized as follows : 1 . Chapter 1 is the introduction part of this paper , expounds the research background of this paper , and points out the research direction of VaR based on systematic analysis of the present situation of VaR research , and finally puts forward the problems to be solved in this paper , and the significance and innovation of the research .
In chapter 3 , we introduce the concept , characteristics and classification of risk management in financial markets , and analyze the risk measurement methods and historical evolution of financial markets , and the measurement framework of financial market risk .
Based on the likelihood ratio test , at 95 % and 99 % confidence level , VaR based on APD distribution is the best model .
In the dynamic quantile test , although the APD distribution has a great advantage over other probability distribution functions , it is quite different from the likelihood ratio test results . At the level of 95 % confidence level , only a small number of models are qualified , whereas at 99 % confidence level , there is no model which is acceptable . Therefore , we can not observe the true VaR value .

The characteristics and innovations of this paper are : the dynamic VaR analysis framework based on APD distribution is put forward , and the APD - VaR parameter model based on profit and loss is applied to show that APD distribution can effectively improve the forecasting quality of VaR ;
In this paper , we put forward the risk measurement retrospective test system combining likelihood ratio test and dynamic quantile test . The author tries to provide some valuable information to the improvement of VaR theory and application in VaR modeling and VaR test .

【学位授予单位】：西南财经大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F830.9;F224

【共引文献】