Operational risk is becoming a major part of corporate governance in companies, especially in the financial services industry. In this paper, we review some of the existing methods used to quantify operational risks in the banking and insurance industries. These methods use recent statistical concepts such as extreme value theory and copula modeling. We explore the possibility of using a coherent risk measure – expected shortfall (ES) – to quantify operational risk. The suitability of the suggested risk measures has been investigated with the help of simulated data sets for two business lines. The generalized Pareto distribution is used for modeling the tails, and three distributions – lognormal, Weibull and Gamma – are used for the body data. Our results show that ES under all three distributions tends to be significantly larger than value-at-risk, which may lead to overestimating the operational loss and consequently overestimating the capital charge. However, the modified ES seems to provide a better way of mitigating any overestimation.

中文翻译：

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操作风险的量化：对连贯风险措施的统计见解

操作风险正在成为公司公司治理的重要组成部分，尤其是在金融服务行业。在本文中，我们回顾了一些用于量化银行业和保险业操作风险的现有方法。这些方法使用了最近的统计概念，例如极值理论和 copula 建模。我们探讨了使用一致的风险衡量指标——预期短缺 (ES)——来量化运营风险的可能性。已在两个业务线的模拟数据集的帮助下调查了建议的风险措施的适用性。广义帕累托分布用于建模尾部，三种分布——对数正态分布、威布尔分布和伽玛分布——用于身体数据。我们的结果表明，所有三种分布下的 ES 往往显着大于风险价值，这可能导致高估运营损失，从而高估资本支出。然而，修改后的 ES 似乎提供了一种更好的方法来减轻任何高估。