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

A risk analyst models losses above a high threshold u using the peaks-over-threshold (POT) approach. According to the Pickands-Balkema-de Haan theorem, which distribution do the excesses over a sufficiently high threshold converge to?

Excesses over a sufficiently high threshold converge to the generalized Pareto distribution. This is the Pickands-Balkema-de Haan result, and it is why POT models fit a GPD to the exceedances rather than a block-maxima distribution or a normal or lognormal form.

  1. AGeneralized Pareto distributionCorrect
  2. BGumbel distribution only
  3. CStudent t distribution
  4. DLognormal distribution

Explanation

The Pickands-Balkema-de Haan theorem states that, for a wide class of underlying distributions, the distribution of excesses over a high threshold converges to the generalized Pareto distribution (GPD). The Gumbel is a special case of the generalized extreme value family used for block maxima, not the POT limit.

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