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

CHAPTER 6

Loss Distributions

Representing a stream of uncertain operational losses with a specified model is a difficult task. Data can be wrongly recorded, fuzzy, incomplete (e.g., truncated or censored), or simply limited. Two main approaches may be undertaken:

1. Nonparametric approach. One approach would be to directly use the empirical density of the data or its smoothed curve version.¹⁴⁶This nonparametric approach can be relevant in two circumstances: first, when the available data are not believed to follow any conventional distribution,¹⁴⁷and second, when the data set available at hand is believed to be sufficiently comprehensive.¹⁴⁸

2. Parametric approach. The task is considerably simplified if we can fit a curve of a simple analytical form that satisfies certain properties. The general goal of this parametric approach is to find a loss distribution that would most closely resemble the distribution of the loss magnitudes of the available data sample.

Figure 6.1 shows a common histogram for the operational loss data with a fitted continuous curve. A visual examination suggests that magnitudes of the majority of the losses are very close to zero, as is seen from the high peak around zero of the histogram. An insignificant fraction of data account for the long right tail of the histogram. Clearly, if we choose the parametric approach and if the fitted curve represents a density of some chosen parametric distribution, the loss distributions that would be adequate for modeling ...