# Modelling the Frequency of Operational Risk Losses under the Basel II Capital Accord: A Comparative study of Poisson and Negative Binomial Distributions

Masters Thesis

Silver, Toni O. 2013. Modelling the Frequency of Operational Risk Losses under the Basel II Capital Accord: A Comparative study of Poisson and Negative Binomial Distributions. Masters Thesis University of East London Royal Docks Business School
Authors Silver, Toni O. Masters Thesis 2013 dissertation for MSc in Finance and Risk Management. Selected by academic staff as a good example of a masters level dissertation. This study investigated the two major methods of modelling the frequency ofoperational losses under the BCBS Accord of 1998 known as Basel II CapitalAccord. It compared the Poisson method of modelling the frequency oflosses to that of the Negative Binomial. The frequency of operational losseswas investigated using a cross section of secondary data published by theBanking for International Settlements (BIS) collected in the 2002 Loss DataCollection Exercise for Operational Risk. The population of the studycomprised all financial institutions in the four Basel II regions of Europe,Australasia, North and South America, and Asia. The sample consisted of theentire 89 banks (census) from 19 countries worldwide that participated inthe 2002 LDCE which reported a total of 47,269 individual loss events above-related questions were investigated:1. Is there a significant difference in the use the Poisson or Negativebinomial distributions in modelling the frequency of operational risklosses?2. Under what conditions should we adopt one for the other?The Chi Square Goodness of fit test was carried out to test the followingstatistical hypotheses at 5% significant level:1. H0 (Null hypothesis): the frequency of operational losses in banksfollows the Poisson distribution.2. H1 (Alternative hypothesis): the frequency of operational losses inbanks does not follow the Poisson distribution.3. H0 (Null hypothesis): the frequency of operational losses in banksfollows the Negative Binomial distribution.4. H1 (Alternative hypothesis): the frequency of operational losses inbanks does not follow the Negative Binomial distribution.15 | U 1 0 4 3 8 5 3The Poisson and the NBD models were fitted to the daily number of lossevents on 3 of the 8 business lines. The models were at first fitted on theoverall data aggregated daily; it then went further to fit the models onCorporate Finance, Trading and Sales, and Retail Banking. The statisticalsoftware used to fit the data was the XLSTAT 2013 and the EASYFIT 5.5Professional edition. Findings from the study confirmed that there is asignificant difference in the use of Poisson and negative binomial inmodelling frequency of operational loss events; while the Poisson model fitson all data, the NBD only fits on a minority of the distributions. It wentfurther to investigate whether there are certain conditions upon which onemodel can be more suitable than the other. It concluded that there is noevidence that supports the conditions upon which one model could beadopted in favour of the other. It also found no evidence to support the useof the relationship between the mean variance of 2013 2013_MSc_Silver.pdfLicenseCC BY-ND Sep 2013 12 Nov 2013

https://repository.uel.ac.uk/item/85w68

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