BACKTESTING EXPECTED SHORTFALL Introducing three model-independent, non-parametric back-test methodologies for Expected Shortfall-猫眼课题宝

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2014

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C. Acerbi;B. Székely

2011年发现预期缺口（ES）是不可引出的，这一发现扩散了它无法回溯测试的错误信念。这种误解引起了对巴塞尔委员会最近决定不顾V aR而采用ES的一些批评。我们以各种方式参与了这场辩论。首先，我们引入了三种无模型、非参数的预期缺口回测方法，这些方法被证明比巴塞尔V - aR测试更强大。这些测试通常需要存储更多的信息，但不引入任何概念限制或计算困难。其中一个提议的测试甚至不需要存储额外的数据。其次，我们观察到，可获得性实际上与模型选择有关，而与模型测试无关，因此与监管风险标准的选择无关。最后，我们表明，在实践中，ES可以与var共同引出，但是，虽然这可能会成为模型选择目的的有用结果，但我们仍然相信，它不会在任何方面影响监管辩论。“Eliciwhat ?”风险专业人士直到2011年才听说可获得性，当时[13]证明了与风险价值（var）相反，预期缺口（ES）是不可获得的。这一结果引发了一场令人困惑的辩论。简单地说，如果一个随机变量Y的统计数据ψ(Y)使评分函数S的期望值最小化，那么它就是可得到的：ψ = arg min x E[S(x， Y)]给定了随机变量的统计数据和实现yt的点预测历史xt，这就提供了一种自然的方法来评估预测模型，通过要求平均分数

The discovery in 2011 that the Expected Shortfall (ES) is not elicitable, diffused the erroneous belief that it could not be backtested. This misconception aroused a number of criticisms to the recent decision of the Basel Committee to adopt ES in spite of V aR. We contribute to this debate in various ways. First of all, we introduce three model–free, nonparametric backtest methodologies for Expected Shortfall which are shown to be more powerful than the Basel V aR test. These tests generally require the storage of more information, but introduce no conceptual limitations nor computational difficulties of any sort. One of the proposed tests doesn’t even require the storage of additional data. Secondly, we observe that elicitability has in fact to do with model selection and not with model testing, and is therefore irrelevant for the choice of a regulatory risk standard. Finally, we show that ES can in practice be jointly elicited with V aR, but while this may turn out to be a useful result for model selection purposes, we remain convinced that it will not impact the regulatory debate in any respect. “Eliciwhat?” Risk professionals had never heard of elicitability until 2011, when [13] proved that Expected Shortfall (ES) is not elicitable as opposed to Value at Risk (V aR). This result sparked a confusing debate. Put it simply, a statistics ψ(Y ) of a random variable Y is said to be elicitable if it minimizes the expected value of a scoring function S: ψ = arg min x E[S(x, Y )] Given a history of point predictions xt for the statistics and realizations yt of the random variable, this provides a natural way to evaluate the forecast model, by requiring that the mean score

BACKTESTING EXPECTED SHORTFALL Introducing three model-independent, non-parametric back-test methodologies for Expected Shortfall

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