Operational Risk: A Guide to Basel II Capital Requirements, Models, and Analysis

CHAPTER 13

Modeling Dependence

In earlier chapters we talked about modeling operational risk data that belongs to a particular business line and a particular loss type combination. If a typical internationally active bank has eight business lines and seven event types,²⁸⁷then there are a total of 56 such combinations. The question is how to aggregate these risks (e.g., measured by value-at-risk) to produce a consolidated capital charge amount. Would a simple summation of the risk measures be the right solution?²⁸⁸But this implies a perfect correlation across groups and suggests that all losses are driven by one single source of randomness instead of multiple independent sources for each of the 56 business line/event type combinations. If this is not the case (and generally, one would expect there to be a certain degree of dependence among groups), then a simple summation would yield an overstated measure of aggregate risk. In this case, one should account for dependence across different business line/event type combinations. According to Chapelle, Crama, Hübner, and Peters (2004), taking dependence into account may substantially reduce the required capital charge, by a factor ranging from 30% to 40%.

Under the recent Basel II guidelines, the advanced measurement approaches (AMA) to measuring the operational risk capital charge are allowed to account for the correlations:

Risk measures for different operational risk estimates must be added for purposes of calculating the regulatory ...