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FRM Part II · FRM Exam Part II · Parametric Approaches (II): Extreme Value

A bank's risk team compares the GEV block maxima approach with the peaks-over-threshold (POT) approach for estimating extreme losses. Which statement is correct?

The peaks-over-threshold approach is generally more data-efficient because it uses every loss above a high threshold, while GEV block maxima keep only the largest loss per block. Both are linked through the same tail index, and POT does not require a zero tail index.

  1. APOT typically uses data more efficiently because it uses all observations exceeding a high threshold, rather than only one maximum per blockCorrect
  2. BGEV uses all exceedances over a threshold while POT uses only one observation per block
  3. CPOT requires the tail index to be zero, while GEV allows any value
  4. DGEV and POT are unrelated because POT is based on the normal distribution

Explanation

Block maxima discard all but the largest observation per block, wasting data. POT uses every observation above a threshold, modelled by the generalized Pareto distribution, and is generally more data-efficient. The two approaches are linked by the same tail index.

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