金融风险管理模型的设定检验—对VaR和CVaR模型的Portmanteau检验和非参数检验

The last several decades have witnessed quite a few financial crises caused by financial risks. As a result, financial risk has become the focus of financial institutions and regulators. Since then risk management models such as Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR) gain their popularity. However, there are few tests available on the correct specification of such models. If a model is incorrectly specified, then the implied risk measures can be far from their true values. This project aims to propose two classes of tests for the correct specification of risk management models, namely Portmanteau tests and nonparametric tests based on empirical distributions. Simplicity is the main feature of the first class, while the second class has better power performance. As VaR and CVaR are defined upon the tail part of a conditional return distribution, we are going to tailor our tests specifically for the tail part instead of the whole distribution, so that our tests can have better size performance. Meanwhile, we are going to propose different methods to deal with the nuisance-parameter problem encountered here. Finally, to highlight the merits of our methods, we apply our proposed tests to some stock indices, stock returns and exchange rates data.

金融市场风险目前已成为全球金融机构和监管当局普遍关注的焦点。在值风险（VaR）、条件在值风险（CVaR）等风险计量技术被广泛应用于金融风险评估,但是少有研究检验这些风险模型的设定正确与否。而错误的模型设定可以使估算出的风险值严重偏离真实值。本项目针对风险管理中常用的VaR和CVaR模型，提出两大类检验风险模型设定的方法：一类是简单易行的Portmanteau检验，一类是具有高检验效能的基于经验分布的非参数检验。针对VaR和CVaR定义于收益分布尾部的特点，我们创新性地将检验统计量构建于分布的尾部而不是整个分布,使检验的实际水准更接近于名义水准。同时我们将有效地解决检验中出现的有碍参数(nuisance-parameter)问题。最后，我们将提出的检验方法应用于证券指数、股票、汇率等数据，对实际应用中的风险模型设定与选择给出指导性建议。

金融市场风险目前已成为全球金融机构和监管当局普遍关注的焦点。在值风险（VaR）、条件在值风险（CVaR）等风险计量技术被广泛应用于金融风险评估,但是少有研究检验CVaR风险模型的设定正确与否。而错误的模型设定可以使估算出的风险值严重偏离真实值。..本项目针对风险管理中常用的VaR和CVaR模型，提出了两大类检验风险模型设定的方法：一类是简单易行的Portmanteau检验，一类是具有高检验效能的基于经验分布的非参数检验。我们推导出了两类检验的渐进分布性质，并且通过蒙特卡洛模拟研究了它们的有限样本表现。..我们有效的解决了检验中有碍参数的影响问题。对于非参数检验，我们推导出了有碍参数项在什么条件下会消失，一旦其消失，我们构造了一个有很强检验效能、标准极限分布的检验方法。而当有碍参数项不消失时，我们通过一个简单的乘子Bootstrap方法来近似其极限分布。对于Portmanteau检验，由于其简单性，我们得到了参数估计影响的具体表达式，进而构造了有碍参数稳健的检验统计量。我们还提出了一种数据驱动方法来选择Portmanteau检验中的滞后阶数。..通过将这些方法应用于全球三大股票指数，我们发现在2007年金融危机期间，VaR模型无法识别出金融危机时期与正常时期市场风险模型的差异，而CVaR模型则可以。..对于CVaR风险模型的条件覆盖检验，填补了该方面的空白，最终结果发表在顶级期刊Management Science。非参数检验的相关成果发表于Econometric Reviews, Econometrics Journal以及Stata Journal等国际著名期刊。.