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

Doctoral thesis English OPEN
Silver, Toni O. (2013)

2013 dissertation for MSc in Finance and Risk Management. Selected by academic staff as a good example of a masters level dissertation. \ud \ud This study investigated the two major methods of modelling the frequency of\ud operational losses under the BCBS Accord of 1998 known as Basel II Capital\ud Accord. It compared the Poisson method of modelling the frequency of\ud losses to that of the Negative Binomial. The frequency of operational losses\ud was investigated using a cross section of secondary data published by the\ud Banking for International Settlements (BIS) collected in the 2002 Loss Data\ud Collection Exercise for Operational Risk. The population of the study\ud comprised all financial institutions in the four Basel II regions of Europe,\ud Australasia, North and South America, and Asia. The sample consisted of the\ud entire 89 banks (census) from 19 countries worldwide that participated in\ud the 2002 LDCE which reported a total of 47,269 individual loss events above\ud -related questions were investigated:\ud 1. Is there a significant difference in the use the Poisson or Negative\ud binomial distributions in modelling the frequency of operational risk\ud losses?\ud 2. Under what conditions should we adopt one for the other?\ud The Chi Square Goodness of fit test was carried out to test the following\ud statistical hypotheses at 5% significant level:\ud 1. H0 (Null hypothesis): the frequency of operational losses in banks\ud follows the Poisson distribution.\ud 2. H1 (Alternative hypothesis): the frequency of operational losses in\ud banks does not follow the Poisson distribution.\ud 3. H0 (Null hypothesis): the frequency of operational losses in banks\ud follows the Negative Binomial distribution.\ud 4. H1 (Alternative hypothesis): the frequency of operational losses in\ud banks does not follow the Negative Binomial distribution.\ud 15 | U 1 0 4 3 8 5 3\ud The Poisson and the NBD models were fitted to the daily number of loss\ud events on 3 of the 8 business lines. The models were at first fitted on the\ud overall data aggregated daily; it then went further to fit the models on\ud Corporate Finance, Trading and Sales, and Retail Banking. The statistical\ud software used to fit the data was the XLSTAT 2013 and the EASYFIT 5.5\ud Professional edition. Findings from the study confirmed that there is a\ud significant difference in the use of Poisson and negative binomial in\ud modelling frequency of operational loss events; while the Poisson model fits\ud on all data, the NBD only fits on a minority of the distributions. It went\ud further to investigate whether there are certain conditions upon which one\ud model can be more suitable than the other. It concluded that there is no\ud evidence that supports the conditions upon which one model could be\ud adopted in favour of the other. It also found no evidence to support the use\ud of the relationship between the mean variance of
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1. INTRODUCTION Sequel to major catastrophic operational losses (Barings Bank, 1995; Enron, 2001; Allied Irish Bank, 2002; National Australia Bank, 2004; Nationwide,

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