The accurate modeling of operational risk is important for banks and the finance industry as a whole to prepare for potentially catastrophic losses. One modeling approach is the loss distribution approach, which requires a bank to group operational losses into risk categories and select a loss frequency and severity distribution for each category. The annual operational loss distribution is estimated as a compound sum of losses from all risk categories, and a bank must set aside capital, called regulatory capital (RC), equal to the 99.9% quantile of this estimated distribution. In practice, this approach may produce unstable RC from year to year as the selected loss severity distribution family changes. This paper presents truncation probability estimates for loss severity data and a consistent quantile scoring function on annual loss data as useful severity distribution selection criteria that may stabilize RC. In addition, the sinh–arcsinh distribution is another flexible candidate family for modeling loss severities that is easily estimated using the maximum likelihood approach. Finally, we recommend that loss frequencies below the minimum reporting threshold be collected so that loss severity data can be treated as censored data.

中文翻译：

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选择损失严重性分布来模拟操作风险

操作风险的准确建模对于银行和整个金融业为潜在的灾难性损失做好准备非常重要。一种建模方法是损失分布法，它要求银行将运营损失分为风险类别，并为每个类别选择损失频率和严重程度分布。年度运营损失分布估计为所有风险类别损失的复合总和，银行必须留出资本，称为监管资本 (RC)，等于该估计分布的 99.9% 分位数。在实践中，随着所选损失严重性分布族的变化，这种方法可能会逐年产生不稳定的 RC。本文提出了损失严重性数据的截断概率估计和年度损失数据的一致分位数评分函数，作为可以稳定 RC 的有用的严重性分布选择标准。此外，sinh-arcsinh 分布是另一个用于建模损失严重性的灵活候选系列，可以使用最大似然方法轻松估计。最后，我们建议收集低于最小报告阈值的损失频率，以便将损失严重性数据视为删失数据。