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

An analyst studies the largest daily loss in each of many 20-day blocks for a trading portfolio. According to the Fisher-Tippett-Gnedenko theorem, if the properly normalised block maxima converge to a non-degenerate distribution, that limiting distribution belongs to which family?

Block maxima that converge after normalisation converge to the generalised extreme value family, covering Gumbel, Frechet and Weibull types. The generalised Pareto distribution applies instead to exceedances over a high threshold, not to block maxima, and the limit is not normal or Student t.

  1. ANormal distribution family
  2. BGeneralised extreme value (GEV) familyCorrect
  3. CGeneralised Pareto family
  4. DStudent t family

Explanation

The Fisher-Tippett theorem states that normalised maxima of i.i.d. observations converge to the GEV family (Gumbel, Frechet or Weibull types). The generalised Pareto distribution describes threshold exceedances (peaks over threshold), not block maxima, so it is the key distractor.

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