Forecasting Value at Risk and Expected Shortfall Using a Semiparametric Approach Based on the Asymmetric Laplace Distribution

Value at Risk (VaR) forecasts can be produced from conditional autoregressive VaR models, estimated using quantile regression. Quantile modeling avoids a distributional assumption, and allows the dynamics of the quantiles to differ for each probability level. However, by focusing on a quantile, these models provide no information regarding expected shortfall (ES), which is the expectation of the exceedances beyond the quantile. We introduce a method for predicting ES corresponding to VaR forecasts produced by quantile regression models. It is well known that quantile regression is equivalent to maximum likelihood based on an asymmetric Laplace (AL) density. We allow the density's scale to be time-varying, and show that it can be used to estimate conditional ES. This enables a joint model of conditional VaR and ES to be estimated by maximizing an AL log-likelihood. Although this estimation framework uses an AL density, it does not rely on an assumption for the returns distribution. We also use the AL log-likelihood for forecast evaluation, and show that it is strictly consistent for the joint evaluation of VaR and ES. Empirical illustration is provided using stock index data. Supplementary materials for this article are available online.     

基于CAViaR模型的沪深300股指期货隔夜风险研究

期货隔夜风险的防范历来是投资者关注的热点,本文以沪深300股指期货为研究对象,采用CAViaR模型对普通隔夜风险进行度量,同时还采用新建的CAViaR-EVT模型对极端隔夜风险进行预测,全面地分析了多头VaR和空头VaR在不同分位数的动态变化特征,最后采用Kupiec似然比检验和动态分位数检验对模型进行后测检验。实证结果表明,隔夜收益序列具有右偏、无长期记忆性和尖峰厚尾等典型特征;CAViaR模型对股指期货的普通隔夜风险具有优异的预测能力,其中AS模型的预测效果最好;加入极值理论后,CAViaR-EVT模型同样能很好地刻画极端分位数下隔夜风险的动态演化过程,且其预测结果比EVT和GARCH-EVT模型要更合理。     

基于CAViaR模型的汇率隔夜风险研究

针对目前缺乏美元当日汇率对其他汇率市场隔夜风险影响的研究,本文在CAViaR模型中的AS模型和SAV模型基础上提出隔夜-AS模型和隔夜-SAV模型来测量汇率隔夜风险,并对日元汇率,人民币汇率和港币汇率2009年到2014年的数据进行实证分析,研究结果表明隔夜-AS模型和隔夜-SAV模型均优于AS模型和SAV模型,且隔夜-AS模型又优于隔夜-SAV模型。这三个汇率的隔夜风险均受到滞后风险的影响,且人民币汇率所受滞后风险最大,美元指数的波动都将加大这三个汇率市场的隔夜风险,美元对日元和港币汇率的冲击大于对人民币汇率的冲击,美元走弱对这三个市场隔夜风险影响大于美元走强所带来的影响,这些都为我国汇率隔夜风险的管理提供了新的方法和思路。     

国际碳市场风险价值度量的新方法——基于EVT-CAViaR模型

受全球经济、政治、能源和政策等各方面因素影响,碳资产价格波动剧烈,探寻适合碳市场风险度量的计量方法具有重要的现实意义。论文以EUA和CER市场为研究对象,对比了CAViaR与GARCH-GED模型在不同预测区间、不同置信水平下度量碳市场风险时的表现,发现CAViaR模型在模型拟合和预测方面要优于GARCH-GED模型,但由于CER市场具有更大的不确定性,导致了CAViaR模型在CER市场的预测表现比EUA市场更差,并且在预测1%VaR时,CAViaR模型表现出不稳定性;论文进一步将EVT与CAViaR模型结合来改进碳市场1%VaR的预测效果,发现在处理具有高风险预测区间以及高风险的CER市场,EVT-CAViaR模型的预测表现都更加稳健,说明该方法能够一定程度上提升碳市场风险的预测精度。     

A quasi-Bayesian model averaging approach for conditional quantile models

The value at risk (VaR) is a risk measure that is widely used by financial institutions to allocate risk. VaR forecast estimation involves the evaluation of conditional quantiles based on the currently available information. Recent advances in VaR evaluation incorporate conditional variance into the quantile estimation, which yields the conditional autoregressive VaR (CAViaR) models. However, uncertainty with regard to model selection in CAViaR model estimators raises the issue of identifying the better quantile predictor via averaging. In this study, we propose a quasi-Bayesian model averaging method that generates combinations of conditional VaR estimators based on single CAViaR models. This approach provides us a basis for comparing single CAViaR models against averaged ones for their ability to forecast VaR. We illustrate this method using simulated and financial daily return data series. The results demonstrate significant findings with regard to the use of averaged conditional VaR estimates when forecasting quantile risk.     

石油期货收益率的分位数建模及其影响因素分析

石油期货收益率的分位数反映了收益率分布特征和石油市场风险特征,有必要建模考察分位数的变化模式与影响因素。针对现有研究在模型方法和分析角度上的不足,本文考虑分位数受市场冲击影响而产生的非线性自回归特征,提出门限CAViaR模型并用以分析石油期货收益率的分位数及其影响因素。基于1998-2009年布伦特原油期货价格的研究表明,石油期货收益率的分位数具有自回归特征并受前期油价涨跌的不对称影响,且油价下跌的作用更强。左尾分位数受油价涨跌的共同影响,而右尾分位数仅受油价下跌的影响,二者呈现不同特征。此外,本文通过考察分位数的动态变化模式揭示了油价风险特征,具有重要的风险管理作用。