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FRM Part I · FRM Exam Part I · Operational Risk

When fitting severity distributions to operational loss data, banks often find that a single lognormal fits the body of the data poorly in the extreme tail. Which approach is commonly used to address this using extreme value theory?

Banks commonly apply extreme value theory by fitting a generalized Pareto distribution to losses above a high threshold, the peaks-over-threshold method. This captures heavy tail behavior that drives capital, whereas a Poisson describes frequency and truncation or averaging would discard the tail.

  1. AFit a generalized Pareto distribution to losses exceeding a high thresholdCorrect
  2. BFit a Poisson distribution to losses below a low threshold
  3. CReplace the severity distribution with the mean loss
  4. DTruncate all losses above the 95th percentile

Explanation

The peaks-over-threshold method models exceedances above a high threshold with a generalized Pareto distribution, capturing heavy tails. Poisson is a frequency model, and truncating or using the mean discards the tail information that drives capital.

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