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

A risk analyst wants to estimate the probability that two equity indices will both suffer extreme losses in the same period. Which multivariate extreme value theory (EVT) feature is designed to capture this dependence in the tails, as opposed to the dependence in the center of the joint distribution?

Tail dependence modeled through an extreme value copula is correct. Multivariate EVT focuses on joint extremes, and copulas describe how tails co-move. Linear correlation reflects the whole distribution and the Hill estimator or block size only describes marginal tails, so neither captures joint tail dependence.

  1. ALinear correlation coefficient estimated on all observations
  2. BTail dependence modeled through an extreme value copulaCorrect
  3. CThe Hill estimator applied to each index separately
  4. DThe block size chosen for each index's block maxima

Explanation

Multivariate EVT models joint tail behavior using extreme value copulas and tail dependence measures. Linear correlation uses the whole distribution and can understate joint extremes. The Hill estimator and block size concern each marginal distribution, not the dependence between them.

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