Comparative analysis of Poisson and alpha-stable distributions on frequency of operational risk loss event

Operational risk events have translated into billions of dollars of losses for financial and insurance institutions. A recent example of an operational risk event was the $7.2 billion trading loss of a capital markets trader, which caused the near collapse of Societe Generale Bank in 2008. The purpose of this quantitative descriptive comparative study is to aid in the decision-making process of allocating capital by examining the underlying probability models. The objective of the study was to compare the Poisson distribution to the alpha-stable probability distribution as a basis for allocating capital for the required capital reserves as mandated by Basel II. The study compares the degree for which the frequency distribution of operational risk loss events adheres to the Poisson distribution and the alpha-stable probability distributions. Using the Operational Riskdata eXchange Association (ORX) operational risk loss events dataset, the analysis within the study included goodness-of-fit tests. The intention of the goodness-of-fit hypothesis test is to identify how well data adhered to probability distributions or compare observed activities to expected activities. The ORX data includes loss figures from European, North American, and Asian financial institutions. The major results of study reveal that the ORX loss events frequencies do not adhere to the Poisson distribution. In making such a conclusion, the study supports the idea that the Poisson distribution is used incorrectly as a foundational model for frequency within operational risk.