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

A risk analyst wants to estimate extreme losses on a trading portfolio using only the observations that are unusually large, rather than splitting the sample into blocks and keeping one maximum per block. Which description best fits the peaks-over-threshold (POT) approach?

The peaks-over-threshold approach fits a generalized Pareto distribution to the amounts by which losses exceed a high threshold. It uses all tail observations rather than one maximum per block, which is the block-maxima GEV method.

  1. AIt fits a generalized Pareto distribution to the amounts by which losses exceed a high thresholdCorrect
  2. BIt fits a generalized extreme value distribution to the largest loss in each block of observations
  3. CIt fits a normal distribution to all losses and scales the result by a tail multiplier
  4. DIt ranks historical losses and reads the quantile directly, with no distribution fitted

Explanation

POT models the exceedances over a high threshold, and the limiting distribution of those exceedances is the generalized Pareto distribution (GPD). Fitting a GEV to block maxima is the alternative extreme value method, so it is not POT. POT uses every observation above the threshold, which makes more efficient use of the tail data than block maxima.

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