The use of GARCH models in VaR estimation

We evaluate the performance of an extensive family of ARCH models in modeling the daily Value-at-Risk (VaR) of perfectly diversified portfolios in five stock indices, using a number of distributional assumptions and sample sizes. We find, first, that leptokurtic distributions are able to produce better one-step-ahead VaR forecasts; second, the choice of sample size is important for the accuracy of the forecast, whereas the specification of the conditional mean is indifferent. Finally, the ARCH structure producing the most accurate forecasts is different for every portfolio and specific to each equity index.     

Evaluating Value-at-Risk Models via Quantile Regression

This article is concerned with evaluating Value-at-Risk estimates. It is well known that using only binary variables, such as whether or not there was an exception, sacrifices too much information. However, most of the specification tests (also called backtests) available in the literature, such as Christoffersen (1998) and Engle and Manganelli (2004) are based on such variables. In this article we propose a new backtest that does not rely solely on binary variables. It is shown that the new backtest provides a sufficient condition to assess the finite sample performance of a quantile model whereas the existing ones do not. The proposed methodology allows us to identify periods of an increased risk exposure based on a quantile regression model (Koenker and Xiao 2002). Our theoretical findings are corroborated through a Monte Carlo simulation and an empirical exercise with daily S&P500 time series.     

Conditional Extremes in Asymmetric Financial Markets

ABSTRACT

The global financial crisis of 2007–2009 revealed the great extent to which systemic risk can jeopardize the stability of the entire financial system. An effective methodology to quantify systemic risk is at the heart of the process of identifying the so-called systemically important financial institutions for regulatory purposes as well as to investigate key drivers of systemic contagion. The article proposes a method for dynamic forecasting of CoVaR, a popular measure of systemic risk. As a first step, we develop a semi-parametric framework using asymptotic results in the spirit of extreme value theory (EVT) to model the conditional probability distribution of a bivariate random vector given that one of the components takes on a large value, taking into account important features of financial data such as asymmetry and heavy tails. In the second step, we embed the proposed EVT method into a dynamic framework via a bivariate GARCH process. An empirical analysis is conducted to demonstrate and compare the performance of the proposed methodology relative to a very flexible fully parametric alternative.     

金融市场典型事实下的风险价值计算及其检验

金融市场典型事实(Stylized facls)的不断涌现,至少表明了有效市场假说并非实际市场波动机制的完美表述.因此,建立在有效市场理论基础之上的主流市场风险(Market risk)测度技术也就无法准确刻画实际市场的波动和风险状况.本文首先提出了对市场风险测度最具价值的三类典型事实,并以上证综指和若干世界主要股市指数为例,探讨了典型事实波动特征下的风险价值(VaR)计算方法,并通过对不同模型假定下所计算的VaR进行规范的后验分析(Backtesting),实证对比了不同波动模型的适用范围和精确程度.     

相依结构、动态系统性风险测度与后验分析

本文利用Copula相依结构理论扩展和求解了现有的系统性风险测度CoVaR,以得到适用于不同类型常参数和时变参数Copula函数及不同分布假设的动态系统性风险测度。为了验证和评估模型设定的准确性与应用价值,我们构建了适用于该动态系统性风险测度CoVaR的严谨后验分析工具。除“无条件覆盖性”、“独立性”和“条件覆盖性”外,我们首次提出了“混合独立性”检验。基于中国14家上市商业银行的实证分析表明：中国上市商业银行与中国银行业之间的相依结构呈现多样化特征;无论是样本内还是样本外预测区间,我们的动态Copula-CoVaR模型能够有效地捕捉典型系统性风险事件;严谨的后验分析不仅需要检验系统性风险测度CoVaR,也需要检验条件事件的临界值VaR。     

系统性风险度量CoES的建模和检验

本文结合极值理论(Extreme Value Theory,EVT)和新的动态混合Copula(Dynamic Mixture Copula,DM-Copula)函数,提出了一种新的CoES估计方法DM-Copula-EVT。在EVT建模中,本文改进了阈值的选取方法以避免选择的主观性,并提出了一系列新的动态混合Copula以更好地刻画金融市场日益复杂的尾部关联性。此外,本文首次提出了检验CoES模型设定正确性的后验分析方法,包括无条件覆盖性检验和条件覆盖性检验。将本文建模和检验方法应用于我国金融市场,研究发现:相对于传统使用的t分布,EVT能更好地拟合指数的尾部分布;新的动态混合Copula函数能更好地刻画金融部门与系统之间的复杂关联性。     

VaR方法在中国股市的实证研究

以上证180指数为实证研究对象,运用三种主要的求VaR方法对中国股市研究,然后利用失败频率检验法对三种方法估计的VaR值的有效性进行后验测试与评估。     

基于藤Copula分组模型的金融市场风险度量研究

传统未分组的藤Copula模型可用于刻画金融资产间的相依性,但其存在将所有不同行业资产视为一个整体的问题。本文在充分考虑金融市场中各机构所属行业不同的基础上,提出了藤Copula分组模型,给出了该模型算法的具体步骤,并证明了算法的收敛性。最后通过返回检验方法,对比研究了藤Copula分组模型和未分组的藤Copula模型对银行业、证券业和保险业间VAR估计的精度差异,结果表明藤Copula分组模型的预测效果更准确且更有效。