Mixing Internal and External Data for Managing Operational Risk

The Loss Distribution Approach has many appealing features since it is expected to be much more risk - sensitive than any other methods taken into consideration by the last proposals by the Basel Committee. Thus this approach is expected to provide significantly lower capital charges for banks whose track record is particularly good relatively to their exposures and compared with industry - wide benchmarks.Unfortunately LDA when calibrated only on internal data is far from being satisfactory from a regulatory perspective as it could likely underestimate the necessary capital charge. This happens for two reasons. First if a bank has experienced a lower - than - average number of events, it will benefit from a lower - than - average capital charge even though its good track record happened by chance and does not result from better - than - average risk management practices. As a consequence, LDA is acceptable as long as internal frequency data are tempered by industry - wide references. As such, it immediately raises the issue of how to cope with both internal frequency data and external benchmarks. This paper proposes a solution based on credibility theory which is widely used in the insurance industry to tackle analogous problems. As a result, we show how to make the statistical adjustment to temper the information conveyed by internal frequency data with the use of external references.Similarly if the calibration of severity parameters ignores external data, then the severity distribution will likely be biased towards low - severity losses since internal losses are typically lower than those recorded in industry - wide databases. Again from a regulatory perspective LDA cannot be accepted unless both internal and external data are merged and the merged database is used in the calibration process. Here again it raises the issue regarding the best way to merge these data. Obviously it cannot be done without any care since if internal databases are directly fuelled with external data, severity distributions will be strongly biased towards high - severity losses. This paper proposes also a statistical adjustment to make internal and external databases comparable with one another in order to permit a safe and unbiased merging