Modeling Correlated Frequencies with Application in Operational Risk Management

Abstract

In this paper, we propose a copula-free approach for modeling correlated frequency distributions using an Erlang-based multivariate mixed Poisson distribution. We investigate some of the properties possessed by this class of distributions and derive a tailormade expectation-maximization algorithm for fitting purposes. The applicability of the proposed distribution is illustrated in an operational risk management context, where this class is used to model the operational loss frequencies and their complex dependence structure in a high-dimensional setting. Furthermore, by assuming that operational loss severities follow the mixture of Erlang distributions, our approach leads to a closed-form expression for the total aggregate loss distribution and its value-at-risk can be calculated easily by any numerical method. The efficiency and accuracy of the proposed approach are analyzed using a modified real operational loss data set.