Modelling Operational Risk Severities with Kernel Density Estimation Using the Champernowne Transformation

Abstract

The subject of this paper is a one-method-fits-all approach to quantify and predict future losses in insurance. This method is based on a semiparametric estimator which is corrected by some nonparametric smoothing techniques. A number of alternative kernel functions are considered for removing boundary bias, resulting from transforming data with a parametric function to bounded support. We also analyse the crucial point of bandwidth selection in nonparametric statistics and discuss three different bandwidth methods, where two are new to the field. An extensive simulation study is presented between totally eighteen different kernel density estimators, and we also consider a practical application based on operational risk data. Operational risk itself is defined as the risk of loss arising from inadequate or failed internal processes, people and systems or from external events.

Keywords: kernel density estimation, asymptotic theory, bandwidth selection, operational risk