Adding prior knowledge to quantitative operational risk models

Abstract

Our approach is based on the study of the statistical severity distribution of a single loss. We analyze the fundamental issues that arise in practice when modeling operational risk data. We address the statistical problem of estimating an operational risk distribution, both abundant data situations and when our available data is challenged from the inclusion of external data or because of underreporting. Our presentation includes an application to show that failure to account for underreporting may lead to a substantial underestimation of operational risk measures. The use of external data information can easily be incorporated in our modeling approach. The paper builds on methodology developed in Bolance et al. (2012b). 1. Quantifying Operational Risk Guided by Prior Knowledge Operational risk is one of the risks that are incorporated in the Basel II regulatory framework for financial institutions and in the Solvency II regulatory framework for insurance companies (Gatzert and Wesker, 2012 and Ashby, 2011), hence the importance of the modelization and quantification of this risk. Also, operational risk is important in the context of Enterprise Risk Management (Hoyt and Liebenberg, 2011 and Dhaene et al. 2012). One major issue addressed in Bolance et al (2012b) is how to incorporate prior knowledge into operational risk models. Such prior knowledge can come in many disguises. One being prior knowledge of parametric shapes of distributions, another being prior knowledge of the frequency of underreporting and a third could be prior knowledge arising from external data sources. The fundamental principles of mixing internal and external operational risk data was originally published in this journal in Gustafsson and Nielsen (2008) and Guillen et al. (2008). Bolance et al. (2012b) take these originally ideas and put them into a broader context, see also the following recent papers proposing alternative methods to quantify operational risk (Cope, E.W., 2012, Cavallo et al., 2012, Feng et al., 2012 and Horbenko et al., 2011). In this paper we show, with a simple example, the effect of incorporating two different types of prior knowledge into the calculation of Value-at-Risk (VaR) and Tail Value-at Risk (TVaR): external operational risk data and expert information about underreporting probability. We 1 We thank the Spanish Ministry of Science / FEDER grant ECO2010-21787-C0301 and Generalitat de Catalunya SGR 1328. Corresponding author: jens.nielsen.1@city.ac.uk 2 We thank the Spanish Ministry of Science / FEDER grant ECO2010-21787-C0301 and Generalitat de Catalunya SGR 1328. Corresponding author: jens.nielsen.1@city.ac.uk