Operational risk measurement: a loss distribution approach with segmented dependence

In the loss distribution approach (LDA), the most widely used approach of operational risk measurement, the modeling dependencies across different risk cells have been extensively studied. However, it has not been recognized that the dependencies between high-frequency, low-impact (HFLI) and low-frequency, high-impact (LFHI) operational risk losses are naturally different. This paper proposes an approach, called the loss distribution approach with segmented dependence (LDA-SD), which can model the different dependencies of HFLI and LFHI losses in the framework of LDA. LDA-SD divides the losses into two parts for HFLI and LFHI, fits their frequency and severity distributions separately and models the segmented dependencies with a copula. In our empirical study, the proposed LDA-SD is applied to measure the operational risk of the overall Chinese banking sector based on the Chinese Operational Loss Database data set, the largest operational risk data set in China. The empirical results reveal that the dependencies are indeed different between HFLI and LFHI losses. The operational risk capital calculated by the LDA-SD is significantly smaller than that calculated by the LDA and considering the holistic dependence, but larger than that simply considering tail dependence.