Empirical likelihood for value-at-risk and expected shortfall
Empirical likelihood for value-at-risk and expected shortfall
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DOI：
10.21314/jor.2008.185
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发表时间：
2008-09
期刊：
影响因子：
0.7
通讯作者：
R. E. Baysal;J. Staum
中科院分区：
文献类型：
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作者：
R. E. Baysal;J. Staum
在估计风险度量时，无论是从历史数据还是通过蒙特卡罗模拟，都需要有置信区间，以提供有关统计不确定性的信息。我们提供了渐近有效的置信区间和置信区域，涉及在险价值（VaR），条件尾部期望和预期亏损（条件VaR），基于三种不同的方法。一个是以前的工作的基础上强大的统计扩展，第二个是一个简单的应用程序的自举，我们得出第三个使用经验的可能性。然后，我们使用金融示例评估模拟实验中置信区间和区域的小样本覆盖率。我们发现，对于大样本量，覆盖概率近似为标称值，但当样本量太小时（大约小于500），覆盖概率明显较低。在这些实验中，新的经验似然方法在中等样本量下提供了最高的覆盖率。我们想衡量一个给定的投资组合的风险，该投资组合在预定的投资期限结束时具有随机利润。我们可以使用基于金融市场随机模型的蒙特卡罗模拟从投资组合的利润分布中进行采样。我们的重点将是根据模拟利润估计投资组合的风险度量，并以置信区间和区域的形式提供有关这些估计的统计不确定性的信息。我们只处理估计风险的蒙特卡罗抽样误差，而不是模型风险，包括使用不正确的金融市场模型引入的误差和从数据估计模型参数的统计误差。我们将强调适度的蒙特卡罗样本量，这是适当的，
When estimating risk measures, whether from historical data or by Monte Carlo simulation, it is helpful to have confidence intervals that provide information about statistical uncertainty. We provide asymptotically valid confidence intervals and confidence regions involving value-at-risk (VaR), conditional tail expectation and expected shortfall (conditional VaR), based on three different methodologies. One is an extension of previous work based on robust statistics, the second is a straightforward application of bootstrapping, and we derive the third using empirical likelihood. We then evaluate the small-sample coverage of the confidence intervals and regions in simulation experiments using financial examples. We find that the coverage probabilities are approximately nominal for large sample sizes, but are noticeably low when sample sizes are too small (roughly, less than 500 here). The new empirical likelihood method provides the highest coverage at moderate sample sizes in these experiments. We want to measure the risk of a given portfolio that has random profits at the end of a predetermined investment period. We can sample from the distribution of the portfolio’s profits using Monte Carlo simulation based on a stochastic model of financial markets. Our focus will be on estimating risk measures for our portfolio based on simulated profits and providing information in the form of confidence intervals and regions about the statistical uncertainty of these estimates. We address only this Monte Carlo sampling error in estimating risk, not the model risk that includes errors introduced by using an incorrect model of financial markets and statistical error in estimating the model’s parameters from data. We will emphasize moderate Monte Carlo sample sizes, which are appropriate when