Operational Value-at-Risk in Case of Zero-inflated Frequency

Abstract

In this paper we analyze operational risk in case of zero-inflated frequency data. We show that standard Poisson distribution does not suit correctly excess zero counts data. Alternatively, Zero-inflated Poisson (ZIP) distribution fits better such data. To assess the benefits of the use of ZIP distribution on operational risk management, we develop two separate aggregate distributions. The first one is based on standard Poisson distribution and the second on ZIP distribution. Note that the severity model is the same for both aggregations. Results show that operational capital charge based on standard Poisson distribution is underestimated by 5% at a very high level of confidence (99.99%).