A Method of Estimating Operational Risk: Loss Distribution Approach with Piecewise-defined Frequency Dependence

In loss distribution approach (LDA), the most popular approach to operational risk aggregation, modeling the dependence across business lines has been recognized, however, the research of separately modeling dependence of high-frequency low-severity and low-frequency high-severity loss events is scarce so far. In this paper, we present an approach to estimate operational risk by modeling frequency dependence for high-frequency low-severity and low-frequency high-severity loss events separately across business lines in the framework of LDA, named LDA with piecewise-defined frequency dependence (LDA-PFD), and then apply this approach to calculate operational risk capital of the overall Chinese banking based on the largest bank, operational risk data set, the Chinese Operational Loss Database (COLD), which consists of 2132 operational risk records. The empirical results reveal that the operational risk capital calculated by LDA-PFD is significantly less than the loss distribution approach simply considering frequency dependence of the entire data (LDA-FD) and loss distribution approach based on piecewise-defined distribution but not considering dependence (LDA-PD).