Operational Risk Modeling in Financial Services

CHAPTER 18Aggregation of Scenarios

18.1 INTRODUCTION

When used for capital calculation, scenarios need to be aggregated. Indeed, not all scenarios will occur the same year, but they cannot either be considered fully independent. As discussed in Part I, the correlation level is one of the main drivers of the final capital number: the typical diversification benefit ranges from 30% to 60% of the sum of the scenario outcomes, when considered at a 1 in 1,000 level.

Correlation assessment is not easy for experts, as the notion of correlation is not always intuitive.

First, what correlation are we talking about? We can think of at least two types of correlations:

1. The occurrences are correlated, that is, the occurrence of A makes the occurrence of B more likely: for instance, a business centre disruption may disorganize temporarily the firm and make the occurrence of fraud more likely.
2. The impacts are correlated, that is, the occurrence of A and B are independent, but should they occur during the same period, their consequences would be correlated, because they are driven by a common factor: for instance, the occurrence of a manual trading error and of an IT disruption may be independent, but their consequences are correlated through market volatility, which drives directly the error loss, and the compensation to corporate clients if the trades are delayed due to IT disruption.

Second, mathematical properties of correlation are not always intuitive. Correlation is not always transitive, ...