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 ...

Get Operational Risk: A Guide to Basel II Capital Requirements, Models, and Analysis now with the O’Reilly learning platform.

O’Reilly members experience books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.