Operational risk modeled analytically II: the consequences of classification invariance

Most of the banks' operational risk internal models are based on loss pooling in risk and business line categories. The parameters and outputs of operational risk models are sensitive to the pooling of the data and the choice of the risk classification. In a simple model, we establish the link between the number of risk cells and the model parameters by requiring invariance of the bank's loss distribution upon a change in classification. We provide details on the impact of this requirement on the domain of attraction of the loss distribution, on diversification effects and on cell risk correlations.