Estimation of the marginal expected shortfall: the mean when a related variable is extreme
Estimation of the marginal expected shortfall: the mean when a related variable is extreme
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DOI：
10.1111/rssb.12069
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发表时间：
2012-09
期刊：
影响因子：
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通讯作者：
J. Cai;J. Einmahl;L. Haan;Chen Zhou
中科院分区：
文献类型：
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作者：
J. Cai;J. Einmahl;L. Haan;Chen Zhou
将金融机构的净资产损失回报率表示为X，将整个市场的净资产损失回报率表示为Y。对于给定的非常小的p>0的值，边际预期短缺（MES）被定义为E{X| Y>QY（1−p）}，其中QY（1−p）是Y分布的第（1−p）个分位数。MES是衡量金融机构系统性风险的一个重要因素。对于一个广泛的非参数类二元分布，我们构造了MES的估计量，并建立了当p↓0时估计量的渐近正态性，因为样本量n→∞。由于我们特别感兴趣的情况下p=O（1/n），我们使用极值技术推导的估计和它的渐近行为。有限样本性能的估计和相关的极限定理中显示了详细的模拟研究。我们还应用我们的方法来估计美国三家大型投资银行的MES。
Denote the loss return on the equity of a financial institution as X and that of the entire market as Y. For a given very small value of p>0, the marginal expected shortfall (MES) is defined as E{X|Y>QY(1−p)} , where QY(1−p) is the (1−p)th quantile of the distribution of Y. The MES is an important factor when measuring the systemic risk of financial institutions. For a wide non‐parametric class of bivariate distributions, we construct an estimator of the MES and establish the asymptotic normality of the estimator when p↓0, as the sample size n→∞. Since we are in particular interested in the case p=O(1/n), we use extreme value techniques for deriving the estimator and its asymptotic behaviour. The finite sample performance of the estimator and the relevance of the limit theorem are shown in a detailed simulation study. We also apply our method to estimate the MES of three large US investment banks.