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

A risk team applies a peaks-over-threshold model to the losses of two portfolios and finds both have a heavy-tailed marginal with tail index (xi) near 0.3. They then fit a model for the joint tail. Which conclusion about practical implementation is most appropriate?

Fit the marginal tails and the dependence structure separately, while recognizing that dependence estimates are highly uncertain because joint extreme exceedances are scarce. Similar marginal tail indices do not imply tail dependence, and dependence cannot be ignored when assessing joint extreme risk.

  1. AFit marginals and dependence separately, recognizing that scarce joint exceedances make dependence estimates highly uncertainCorrect
  2. BJoint tail estimates are more reliable than marginal ones because they use both datasets
  3. CBecause both xi values are equal, the portfolios must be perfectly tail dependent
  4. DBecause xi is positive, the dependence structure can be ignored

Explanation

Joint extreme observations are very rare, so the dependence in the tail is estimated from few points and is uncertain. Equal marginal tail indices say nothing about the dependence. Ignoring dependence would misstate joint risk.

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