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

An analyst applies the block maxima approach to daily losses, taking the maximum loss in each block of 250 trading days. According to the Fisher-Tippett-Gnedenko theorem, the properly normalized block maxima converge to which distribution family?

Normalized block maxima converge to the generalized extreme value (GEV) distribution, according to the Fisher-Tippett-Gnedenko theorem. The generalized Pareto distribution applies to threshold exceedances instead, so it is the wrong family for block maxima.

  1. AThe generalized extreme value (GEV) distributionCorrect
  2. BThe generalized Pareto distribution
  3. CThe normal distribution
  4. DThe Student t distribution

Explanation

The Fisher-Tippett theorem says normalized maxima of iid observations converge to the GEV family (Gumbel, Frechet, Weibull). The generalized Pareto distribution describes exceedances over a high threshold in the peaks-over-threshold approach, not block maxima. Normal and t are not limiting laws for maxima.

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