FRM Part II · FRM Exam Part II · Risk Measurement and Assessment
A risk analyst fits a severity model to internal loss data and finds that the largest few losses far exceed what a lognormal fit predicts, so the tail appears heavier. Which approach is most appropriate for improving the estimate of high quantiles?
The best approach is to model exceedances over a high threshold with a generalized Pareto distribution, using extreme value theory. It targets tail behavior directly. Deleting the largest losses would understate capital, and improving body fit does not fix the heavy tail.
- AFit a generalized Pareto distribution to losses exceeding a high threshold, using peaks-over-threshold extreme value theoryCorrect
- BReplace the severity distribution with a normal distribution fitted to the log of the frequency
- CRemove the largest losses as outliers and refit the lognormal
- DLower the collection threshold to zero so the lognormal fits the body better
Explanation
Peaks-over-threshold with a generalized Pareto distribution is designed to model tail behavior above a high threshold and handle heavy tails. Removing large losses understates capital, and lowering the collection threshold addresses body data, not tail shape. A normal on log frequency is conceptually confused.
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