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

A risk manager is choosing between the block maxima approach and the peaks-over-threshold (POT) approach for estimating tail risk from 20 years of daily loss data. Which statement correctly describes the two approaches?

Block maxima fits the generalised extreme value distribution to the largest observation in each block, while peaks-over-threshold fits the generalised Pareto distribution to all exceedances over a high threshold. POT generally uses data more efficiently because it keeps all extreme observations, not just one per block.

  1. ABlock maxima fits the generalised Pareto distribution to losses; POT fits the generalised extreme value distribution to maxima of blocks
  2. BBlock maxima fits the generalised extreme value distribution to the maximum of each block; POT fits the generalised Pareto distribution to exceedances over a high thresholdCorrect
  3. CBoth approaches fit the generalised extreme value distribution, differing only in block length
  4. DBoth approaches fit the generalised Pareto distribution, differing only in the confidence level used

Explanation

Block maxima divides data into periods and fits the GEV distribution to each period's maximum. POT takes all losses above a high threshold and fits the generalised Pareto distribution to the excesses. The first option reverses the two, and the other options misstate the distributions used.

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