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

A risk analyst fits a Generalized Extreme Value (GEV) distribution to block maxima of daily portfolio losses, where each block is one month. The estimated tail index ξ is 0.30. Which statement best describes the fitted distribution?

A positive tail index of 0.30 means the GEV is of Fréchet type, which has a heavy, power-law tail. This suits fat-tailed financial losses. Gumbel needs a tail index of zero, Weibull needs a negative one, and block maxima do not converge to a normal distribution.

  1. AIt is a Fréchet-type distribution with a heavy tail, appropriate for fat-tailed loss dataCorrect
  2. BIt is a Gumbel-type distribution with an exponentially decaying tail
  3. CIt is a Weibull-type distribution with a finite upper bound on losses
  4. DIt is a normal distribution because block maxima converge to normality

Explanation

In the GEV family, ξ > 0 corresponds to the Fréchet case, which has a heavy (power-law) tail. ξ = 0 is Gumbel and ξ < 0 is Weibull with a finite endpoint. Block maxima do not converge to the normal distribution, so that option is wrong.

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