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

Which of the following best explains why the GEV approach is useful for estimating extreme risk compared with fitting a normal distribution to all returns?

The GEV models only the block maxima, which converge to a limiting distribution whatever the parent distribution is. The tail estimate therefore does not depend on fitting the centre of the data, unlike a normal fit across all returns.

  1. AIt models only the extreme observations through a limiting distribution, so the tail is not driven by the bulk of the dataCorrect
  2. BIt guarantees that VaR estimates will never be exceeded
  3. CIt requires the underlying returns to be normally distributed
  4. DIt uses all observations equally, giving the most efficient estimate of the centre of the distribution

Explanation

Extreme value theory shows that normalized maxima converge to a GEV regardless of the parent distribution (under regularity conditions), so the tail can be modelled directly without assuming the shape of the whole distribution. It does not eliminate exceedances, and it focuses on extremes rather than the centre.

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