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

CHAPTER 12

Robust Modeling

An actuarial-type model dominates statistical models for operational risk under the advanced measurement approach.²⁶⁴The Basel II Capital Accord requires that a quantitative model for operational risk must have the capacity to accommodate peculiarities of the loss distribution: high kurtosis, severe right-skewness, and excessive heavy-tailedness. Model selection is complicated by scarcity of the available data along with the presence of tail events, the so-called low frequency/high severity losses, that contribute to the heaviness of the upper tail of the loss distribution. Some critics of the Basel II framework argue that the standards required for the calculation of regulatory capital are such that the amount of the capital charge might even exceed the economic capital,²⁶⁵leaving decreased availability of funds required for financial needs and investments.²⁶⁶This may be well due to misspecification in the model. In this chapter, we propose an approach that can provide a solution to this dilemma.

In 2001, the Basel Committee made the following recommendation:

Data will need to be collected and robust estimation techniques (for event impact, frequency, and aggregate operational loss) will need to be developed. (BIS, 2001, Annex 6, p. 26)

The notion of robustness can be given different interpretations. One interpretation would be the distributional robustness—robustness of the assumed model to minor departures from the model assumptions. Outlier-resistant ...