基于分段损失分布法和Copula的银行操作风险集成度量

多个风险单元的集成度量是银行操作风险管理的关键步骤之一。立足于操作风险的“厚尾”、“截断”性,从分段损失分布法的视角出发,探讨操作风险集成度量的模式和数值方法。首先,引入两阶段损失分布法来拟合单个风险单元边际损失分布,用双截尾分布代替传统的完整分布来刻画“高频低损”损失数据的双截断特性,利用POT模型捕获“低频高损”事件的厚尾特性。再次,基于分段建模思路,对传统度量过程中边际分布为单一、完整分布的Copula模型进行了扩展,研究边际分布为分段分布、截尾分布条件下使用Copula函数集成度量操作风险的框架和步骤,并设计了Monte Carlo模拟算法。最后,以实证分析的形式验证所构建模型。通过对中国商业银行416个操作风险损失数据的实证分析,结果表明分段分布、截尾分布能对单个风险单元边际分布有更好的拟合效果,能减小由于分布选择不当而引发的模型风险。分段度量视角下Copula函数的引入能灵活处理多个操作风险单元间的相依结构,使风险度量结果更为合理。

Operational Risk Aggregation Measurement of Banks Basedon PSD-LDA and Copula Function

The aggregated modeling and measuring multidimensional operational risk is a crucial step for operational risk management. Based on the characters of “heavy tail” and “truncation” of operational risk, the model and numerical method of integrated measurement of operational risk are discussed. Firstly, the very popular univariate loss distribution approach is extended to piecewise-defined severity distribution approach(PSD-LDA), doubly-truncated distribution is used for severity distribution fitting of high severity low frequency losses instead of traditional full distributions, and POT model is applied to capture “fat tail” feature of low severity high frequency losses. Secondly, based on PSD-LDA, Copula function is utilized to describe the dependence structure while the single and complete marginal severity distribution of risk cell is replaced by the separated and truncated distribution, and the Monte Carlo simulation algorithm is studied. Last, all the models and methods are tested with 246 operational losses. The results show that the PSD-LDA performs more effectively and stably, and the application of the Copula function has the advantage in capturing dependency structure of multiple risk cells, which allows the allocation of capital and hedge operational risk in a more efficient way than the standard approach.