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Value-at-Risk via mixture distributions reconsidered

机译：重新考虑了通过混合分配的风险价值

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Value-at-Risk (VaR) has evolved as one of the most prominent measures of downside risk in financial markets. Zhang and Cheng [M.-H. Zhang, Q.-S. Cheng, An Approach to VaR for capital markets with Gaussian mixture, Applied Mathematics and Computation 168 (2005) 1079-1085] proposed an approach to VaR for daily returns based on Gaussian mixtures, which have become rather popular in empirical economics and finance since the seminal paper of Hamilton [J.D. Hamilton, A new approach to the economic analysis of nonstationary time series and the business cycle, Econometrica 57 (2) (1989) 357-384]. However, they do not conduct tests to assess the accuracy of the mixture-implied VaR measures. Recently, Guidolin and Timmermann [M. Guidolin, A. Timmermann, Term structure of risk under alternative econometric specifications, Journal of Econometrics, 131 (2006) 285-308] showed that Markov mixture models do well in measuring VaR at a monthly frequency, but the results may not hold for daily returns due to their more pronounced non-Gaussian features. This paper provides an extensive application of various Markov mixture models to VaR for daily returns of major European stock markets, including out-of-sample backtesting. To accommodate the properties of daily returns, we consider both Gaussian and Student's t mixtures, and we compare the performance of both uni- and multivariate models under different parameter updating schemes. We find that a univariate mixture of two Student's t distributions performs best overall. However, by the example of the recent turmoil in financial markets, we also highlight a weak point of the approach.
机译：风险价值（VaR）已演变为金融市场下行风险最重要的衡量指标之一。 Zhang and Cheng [M.-H.张强生Cheng，《一种具有高斯混合的资本市场的VaR方法》，应用数学与计算168（2005）1079-1085]提出了一种基于高斯混合的每日收益的VaR方法，自从汉密尔顿的开创性论文[JD汉密尔顿，一种非平稳时间序列和商业周期的经济分析新方法，《计量经济学》 57（2）（1989）357-384]。但是，他们没有进行测试以评估混合物暗示的VaR量度的准确性。最近，Guidolin和Timmermann [M. Guidolin，A. Timmermann，《替代计量经济学规范下的风险期限结构》，《计量经济学杂志》，131（2006）285-308]显示，马尔可夫混合模型在按月频率测量VaR方面表现良好，但每天的结果可能不成立归因于其更明显的非高斯特征。本文将各种马尔可夫混合模型广泛应用于VaR，以提供主要欧洲股票市场的每日收益，包括样本外回测。为了适应日收益率的属性，我们同时考虑了高斯和学生的t混合，并比较了在不同参数更新方案下单变量和多元模型的性能。我们发现，两个学生t分布的单变量混合总体上表现最佳。但是，以最近金融市场动荡为例，我们也强调了该方法的不足。

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