Operational risk modeled analytically II: the consequences of classification invariance

TL;DR

This paper explores how the classification scheme in operational risk models affects their parameters and outputs, emphasizing the importance of invariance to ensure consistent risk assessment across different classifications.

Contribution

It introduces an analytical framework linking risk cell classification to model parameters, highlighting the impact of classification invariance on loss distribution and diversification.

Findings

Loss distribution invariance constrains model parameters.

Classification affects diversification effects.

Risk correlations depend on classification scheme.

Abstract

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.