英文标题：
《Multinomial VaR Backtests: A simple implicit approach to backtesting
  expected shortfall》
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作者：
Marie Kratz, Yen H. Lok, Alexander J McNeil
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最新提交年份：
2016
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英文摘要：
  Under the Fundamental Review of the Trading Book (FRTB) capital charges for the trading book are based on the coherent expected shortfall (ES) risk measure, which show greater sensitivity to tail risk. In this paper it is argued that backtesting of expected shortfall - or the trading book model from which it is calculated - can be based on a simultaneous multinomial test of value-at-risk (VaR) exceptions at different levels, an idea supported by an approximation of ES in terms of multiple quantiles of a distribution proposed in Emmer et al. (2015). By comparing Pearson, Nass and likelihood-ratio tests (LRTs) for different numbers of VaR levels $N$ it is shown in a series of simulation experiments that multinomial tests with $N\\geq 4$ are much more powerful at detecting misspecifications of trading book loss models than standard binomial exception tests corresponding to the case $N=1$. Each test has its merits: Pearson offers simplicity; Nass is robust in its size properties to the choice of $N$; the LRT is very powerful though slightly over-sized in small samples and more computationally burdensome. A traffic-light system for trading book models based on the multinomial test is proposed and the recommended procedure is applied to a real-data example spanning the 2008 financial crisis.
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中文摘要：
根据交易账簿（FRTB）的基本审查，交易账簿的资本费用基于一致的预期缺口（ES）风险度量，这表明对尾部风险更为敏感。在本文中，有人认为，预期缺口的回溯测试（或计算预期缺口的交易账簿模型）可以基于不同水平的风险价值（VaR）例外情况的同时多项式测试，这一想法得到了埃默等人（2015）提出的分布多个分位数的ES近似值的支持。通过比较Pearson、Nass和似然比测试（LRT）对于不同数量的风险值水平$N$，一系列模拟实验表明，与对应于$N=1$的标准二项式例外测试相比，具有$N\\geq 4$的多项式测试在检测交易账面损失模型的错误指定方面更为强大。每个测试都有其优点：Pearson提供了简单性；Nass的尺寸特性非常稳定，可以选择N$；LRT功能非常强大，但在小样本中尺寸略大，计算负担更重。提出了一种基于多项式检验的交易账簿模型红绿灯系统，并将推荐的程序应用于跨越2008年金融危机的真实数据示例。
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Risk Management        风险管理
分类描述：Measurement and management of financial risks in trading, banking, insurance, corporate and other applications
衡量和管理贸易、银行、保险、企业和其他应用中的金融风险
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一级分类：Quantitative Finance        数量金融学
二级分类：Statistical Finance        统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
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