基于极值理论的资产组合风险研究

在金融系统中风险管理者十分关注投资风险的大小,尤其是在极端情况下的风险大小.市场风险值(VaR)是一种常用的度量风险的方法.本文将极值理论用于中国上证指数和深成指数市场风险值的度量,同时探讨了用极值理论评价资产组合风险的方法,并将其计算结果与基于正态分布同t分布的方法进行比较,发现采用极值理论度量市场风险值要优于经典的方法.     

基于极值分布理论的VaR与ES度量

本文应用极值分布理论对金融收益序列的尾部进行估计,计算收益序列的在险价值VaR和预期不足ES来度量市场风险。通过伪最大似然估计方法估计的GARCH模型对收益数据进行拟合,应用极值理论中的GPD对新息分布的尾部建模,得到了基于尾部估计产生收益序列的VaR和ES值。采用上证指数日对数收益数据为样本,得到了度量条件极值和无条件极值下VaR和ES的结果。实证研究表明:在置信水平很高(如99%)的条件下,采用极值方法度量风险值效果更好。而置信水平在95%下,其他方法和极值方法结合效果会很好。用ES度量风险能够使我们了解不利情况发生时风险的可能情况。     

基于动态E-VaR模型的房地产收益波动性测度研究

基于房地产股票价格数据,针对现有大多数风险测度方法没有考虑到小概率、大损失的极端事件的现状,运用极值理论EVT和在险值VaR构造动态风险计量模型。Back-testing方法检验结果表明,基于动态E-VaR的市场风险测度方法对于指数收益率风险的度量具有较强的适用性。     

国际碳交易市场的风险度量及对我国的启示——基于状态转移与极值理论的VaR比较研究

本文以欧洲气候交易所公布的CERs期货报价为研究对象,将Markov波动转移引入VaR的计算,结合极值理论,度量国际碳交易市场的系统风险。首先建立SWARCH模型与MS-GARCH模型描述价格波动的阶跃特性,直接测算动态VaR。随后采用POT模型拟合标准残差序列的右尾超门限分布,确定极值分位数,再次测算动态VaR。最后通过回测检验选取最优风险值,并由此分析了我国获批碳项目变动趋势与国际碳交易市场风险变动趋势间的关系。     

基于ARIMA—GARCH模型和极值理论的中国股市

以极值理论为基础的风险值度量方法是最近发展起采的最为有效的方法之一，但在传统的单纯采用极值理论的建模过程中对误差项假定为独立同分布的白噪声过程，会对应用极值理论估算风险价值产生一定误差。本文以上证指数和深证成指为例．利用ARIMA—GARCH模型捕获股票收益序列中的自相关和异方差现象，对该模型中残差的条件分布的合理假定进行了实证分析比较．然后利用极值理论对经过ARIMA—GARCH模型筛选过的残差进行极值分析，估算风险价值。     

基于极值理论与蒙特卡洛模拟的商业银行操作风险度量研究

本文以商业银行操作风险的度量为研究目标,以操作风险高级计量法的思想为导向,运用极值理论及银行的损失分布情况对操作风险进行量化研究。极值理论注重模拟收益或损失分布的尾部,而操作风险存在明显的厚尾现象．所以极值理论可以比较有效地解决在操作风险数据较少的客观条件下如何计量操作风险的问题。文章阐述了如何运用极值理论对操作风险求取在险价值（vaR）,且在已有现实数据的情况下,引入蒙特卡洛模拟法扩展数据并进行实证分析,使得所求VaR值更加精确。     

基于GARCH模型的极值VaR风险的动态区间估计模型

为了更准确地度量在险值的估计精度及弥补现有极值VaR测算模型的不足,文章基于GARCH方法推导了极值VaR的动态置信区间估计模型,论述了风险资产的极值VaR假设检验方法及基于GARCH方法的置信区间求法,最后用中信(中信标普300)指数对中国股市风险情况作了区间估计及显著性检验的实证分析。结果表明提出的方法较参数法置信区间有更好的估计精度,且能较为敏感地捕捉收益的动态性。     

基于极值理论和Bootstrap方法的E-VaR研究和实证分析

考虑金融时间序列的厚尾特性,讨论了应用极值理论中的广义Pareto分布模型度量风险的问题。利用Bootstrap和MLE方法对参数进行点估计和区间估计,得出E-VaR的估计值,并对深证综指收益进行实证分析,探讨与尾部相关的极值风险,结果令人满意。     

基于极值理论的新型农村金融机构风险防范研究

本文根据极值理论，分析我国新型农村金融机构的风险，以达到强化金融市场风险识别能力，提升风险度量精度，防患金融风险因果关系效应，增强风险控制的效果。     

基于VaR理论的工程造价风险研究

随着极值统计理论的发展,其在水文、海洋、气象、地震、金融、以及工程等可靠性领域被越来越广泛地应用。文中根据极端事件风险理论和工程造价风险分析的实际,提出了基于POT模型的一种极值分布——GPD,并利用GPD分布,得到相应的VaR(风险价值)估计值,实现对工程造价风险的度量。     

金融资产厚尾分布及常用的风险度量

本文首先运用正态分布、带有位置-尺度参数的t分布、logistic分布、极值分布、-stable分布和核密度估计对上证综指收益率分布进行拟合,结果表明核密度估计优于其他分布。其次,在进行尾部风险拟合和度量风险方面,通过设定相关指标,在显著性水平为1%时,-stable分布更适合衡量风险程度,在此基础上提出了调和-stable分布,并得到一个同构表示解。最后,本文给出了蒙特卡洛-stable分布模拟和经验值下的MDD、DaR和CDaR,并得到了模型值和经验值之间的乘离率。     

Fat tails,VaR and subadditivity

Financial institutions rely heavily on Value-at-Risk (VaR) as a risk measure, even though it is not globally subadditive. First, we theoretically show that the VaR portfolio measure is subadditive in the relevant tail region if asset returns are multivariate regularly varying, thus allowing for dependent returns. Second, we note that VaR estimated from historical simulations may lead to violations of subadditivity. This upset of the theoretical VaR subadditivity in the tail arises because the coarseness of the empirical distribution can affect the apparent fatness of the tails. Finally, we document a dramatic reduction in the frequency of subadditivity violations, by using semi-parametric extreme value techniques for VaR estimation instead of historical simulations.     

Measuring extreme risk spillovers across international stock markets: A quantile variance decomposition analysis

This paper proposes a quantile variance decomposition framework for measuring extreme risk spillover effects across international stock markets. The framework extends the spillover index approach suggested by Diebold and Yilmaz (2009) using a quantile regression analysis instead of the ordinary least squares estimation. Thus, the framework provides a new tool for further study into the extreme risk spillover effects. The model is applied to G7 and BRICS stock markets, from which new insights emerged as to the extreme risk spillovers across G7 and BRICS stock markets, and revealed how extreme risk spillover across developed and emerging stock markets. These findings have important implications for market regulators.     

The t Copula and Related Copulas

The t copula and its properties are described with a focus on issues related to the dependence of extreme values. The Gaussian mixture representation of a multivariate t distribution is used as a starting point to construct two new copulas, the skewed t copula and the grouped t copula, which allow more heterogeneity in the modelling of dependent observations. Extreme value considerations are used to derive two further new copulas: the t extreme value copula is the limiting copula of componentwise maxima of t distributed random vectors; the t lower tail copula is the limiting copula of bivariate observations from a t distribution that are conditioned to lie below some joint threshold that is progressively lowered. Both these copulas may be approximated for practical purposes by simpler, better-known copulas, these being the Gumbel and Clayton copulas respectively.     

Granger causality in risk and detection of extreme risk spillover between financial markets

Controlling and monitoring extreme downside market risk are important for financial risk management and portfolio/investment diversification. In this paper, we introduce a new concept of Granger causality in risk and propose a class of kernel-based tests to detect extreme downside risk spillover between financial markets, where risk is measured by the left tail of the distribution or equivalently by the Value at Risk (VaR). The proposed tests have a convenient asymptotic standard normal distribution under the null hypothesis of no Granger causality in risk. They check a large number of lags and thus can detect risk spillover that occurs with a time lag or that has weak spillover at each lag but carries over a very long distributional lag. Usually, tests using a large number of lags may have low power against alternatives of practical importance, due to the loss of a large number of degrees of freedom. Such power loss is fortunately alleviated for our tests because our kernel approach naturally discounts higher order lags, which is consistent with the stylized fact that today’s financial markets are often more influenced by the recent events than the remote past events. A simulation study shows that the proposed tests have reasonable size and power against a variety of empirically plausible alternatives in finite samples, including the spillover from the dynamics in mean, variance, skewness and kurtosis respectively. In particular, nonuniform weighting delivers better power than uniform weighting and a Granger-type regression procedure. The proposed tests are useful in investigating large comovements between financial markets such as financial contagions. An application to the Eurodollar and Japanese Yen highlights the merits of our approach.     

Forecasting extreme financial risk: A score-driven approach

This paper develops a new class of dynamic models for forecasting extreme financial risk. This class of models is driven by the score of the conditional distribution with respect to both the duration between extreme events and the magnitude of these events. It is shown that the models are a feasible method for modeling the time-varying arrival intensity and magnitude of extreme events. It is also demonstrated how exogenous variables such as realized measures of volatility can easily be incorporated. An empirical analysis based on a set of major equity indices shows that both the arrival intensity and the size of extreme events vary greatly during times of market turmoil. The proposed framework performs well relative to competing approaches in forecasting extreme tail risk measures.     

Realized extreme quantile: A joint model for conditional quantiles and measures of volatility with EVT refinements

We propose a new framework exploiting realized measures of volatility to estimate and forecast extreme quantiles. Our realized extreme quantile (REQ) combines quantile regression with extreme value theory and uses a measurement equation that relates the realized measure to the latent conditional quantile. Model estimation is performed by quasi maximum likelihood, and a simulation experiment validates this estimator in finite samples. An extensive empirical analysis shows that high‐frequency measures are particularly informative of the dynamic quantiles. Finally, an out‐of‐sample forecast analysis of quantile‐based risk measures confirms the merit of the REQ.     

EVT and tail-risk modelling: Evidence from market indices and volatility series

Value-at-Risk (VaR) has become the universally accepted risk metric adopted internationally under the Basel Accords for banking industry internal control, capital adequacy and regulatory reporting. The recent extreme financial market events such as the Global Financial Crisis (GFC) commencing in 2007 and the following developments in European markets mean that there is a great deal of attention paid to risk measurement and risk hedging. In particular, to risk indices and attached derivatives as hedges for equity market risk. The techniques used to model tail risk such as VaR have attracted criticism for their inability to model extreme market conditions. In this paper we discuss tail specific distribution based Extreme Value Theory (EVT) and evaluate different methods that may be used to calculate VaR ranging from well known econometrics models of GARCH and its variants to EVT based models which focus specifically on the tails of the distribution. We apply Univariate Extreme Value Theory to model extreme market risk for the FTSE100 UK Index and S&P-500 US markets indices plus their volatility indices. We show with empirical evidence that EVT can be successfully applied to financial market return series for predicting static VaR, CVaR or Expected Shortfall (ES) and also daily VaR and ES using a GARCH(1,1) and EVT based dynamic approach to these various indices. The behaviour of these indices in their tails have implications for hedging strategies in extreme market conditions.