Abstract: Choosing a proper loss distribution is the most important step and an important prerequisite to correctly measure operational risks. Based on the “truncation” of operational risk data, the traditional piecewise-defined severity distribution approach (PSD-LDA) which defined loss intensity by stages was extended to a doubly-truncated distributions-POT (DTD-POT) model, which was used to characterize the doubly-truncated characteristics of loss data instead of the traditional single complete distribution. First, the impact of truncated data on the loss of distribution fitting was analyzed. Then the DTD-POT model was proposed, in which both the influence of minimum collection threshold and the cut-off point between HFLS and LFHS were considered. After that, the simulation steps of Monte Carlo were proposed while the separated distribution and truncated distribution were applied instead of the traditional single and complete distribution. Finally, all the models and methods were tested with hand-collected samples of 549 operational losses from 1994 to 2013. The result reveals that compared with PSD-LDA, the DTD-POT model has a better fitting effect on data, a better stability in measurement, and less error caused by improper selection of loss distribution.

Key words: operational risk measurement；truncated , loss data；doubly-truncated distribution；piecewise-defined severity distribution approach (PSD-LDA)；extreme theory

摘要： 选择恰当的损失分布是对操作风险进行度量的首要环节，也是正确度量操作风险的重要前提。立足于操作风险数据的“截断”性，将传统分阶段定义损失强度的损失分布法（PSD-LDA）拓展为双截尾分布-POT（DTD-POT）度量模型，用双截尾分布、分段分布代替传统的单一完整分布来刻画损失数据的双截断特性。首先，综合考虑数据收集门槛值、阈值对分布拟合的影响，构建DTD-POT度量模型，并提出DTD-POT的度量步骤和流程；其次，设计当损失强度分布为分段、截尾分布时使用Monte Carlo模拟度量操作风险的具体步骤；最后，收集我国商业银行1994~2013年的549个风险损失数据，以实证分析的形式验证所提出的方法，并将结果与单一损失分布法、传统的PSD-LDA进行了比较。实证结果表明，PSD-LDA和PTD-POT模型均能较好的拟合损失的主体和尾部，拟合结果显著优于单一损失分布法；此外，和传统的PSD-LDA相比，DTD-POT模型能对数据有更好的拟合效果，度量结果具有较好的稳定性，减少因损失分布选择不当带来的误差。

关键词: 操作风险度量, 截断数据, 双截尾分布, 分段损失分布法, 极值理论