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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%).

If you would like to write for this, or any other Emerald publication, then please use our Emerald for Authors service information about how to choose which publication to write for and submission guidelines are available for all. Please visit www.emeraldinsight.com/authors for more information. About Emerald www.emeraldinsight.comEmerald is a global publisher linking research and practice to the benefit of society. The company manages a portfolio of more than 290 journals and over 2,350 books and book series volumes, as well as providing an extensive range of online products and additional customer resources and services.Emerald is both COUNTER 4 and TRANSFER compliant. The organization is a partner of the Committee on Publication Ethics (COPE) and also works with Portico and the LOCKSS initiative for digital archive preservation. AbstractPurpose -The purpose of this paper is to introduce the zero-modified distributions in the calculation of operational value-at-risk. Design/methodology/approach -This kind of distributions is preferred when excess of zeroes is observed. In operational risk, this phenomenon may be due to the scarcity of data, the existence of extreme values and/or the threshold from which banks start to collect losses. In this article, the paper focuses on the analysis of damage to physical assets. Findings -The results show that basic Poisson distribution underestimates the dispersion, and then leads to the underestimation of the capital charge. However, zero-modified Poisson distributions perform well the frequency. In addition, basic negative binomial and its related zero-modified distributions, in their turn, offer a good prediction of count events. To choose the distribution that suits better the frequency, the paper uses the Vuong's test. Its results indicate that zero-modified Poisson distributions, basic negative binomial and its related zero-modified distributions are equivalent. This conclusion is confirmed by the capital charge calculated since the differences between the six aggregations are not significant except that of basic Poisson distribution. Originality/value -Recently, the zero-modified formulations are widely used in many fields because of the low frequency of the events. This article aims to describe the frequency of operational risk using zero-modified distributions.