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

CHAPTER 9

Truncated Distributions

In an ideal scenario, the data collection process results in all operational loss events being detected and duly recorded. However, the data recording is subject to lower recording thresholds, so that only data above a certain amount enter databases. In this sense, the data available for estimation appear to be left-truncated. Left-truncation of the data must be appropriately addressed in the estimation process, in order to determine a correct capital charge.

In this chapter we discuss a methodology for the estimation of the parameters of the severity and frequency distributions when some operational loss data are missing from the data set. We further explore the implications of using a wrong approach (under which the truncation is ignored) and correct approaches (under which the truncation is adequately treated) on the resulting capital charge and present results of related empirical studies.

REPORTING BIAS PROBLEM

In the 2002 LDCE (Quantitative Impact Study 3) by the Basel Committee, 89 participating banks were asked to report information about the minimum cutoff levels that they used when recording operational loss data. Table 9.1 reports the results. The majority of the banks set the cutoff level at euro 10,000.

While for internal databases the minimum collection threshold is set at approximately euro 10,000, for public (or external) databases and consortiums, the minimum collection threshold is set at approximately $1 million.²¹⁷

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