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FRM Part II · FRM Exam Part II · Integrated Risk Management

A risk manager aggregates operational and credit risk losses using a Gaussian copula calibrated to the overall correlation. A reviewer argues this likely understates joint extreme losses during a crisis. Which is the most appropriate reason?

The reviewer is right because a Gaussian copula exhibits no tail dependence. Even with a sensible overall correlation, it gives too little probability to simultaneous extreme losses across risk types, so crisis-period aggregate capital may be understated. A t-copula would capture more tail dependence.

  1. AA Gaussian copula has no tail dependence, so joint extreme events are assigned too little probabilityCorrect
  2. BA Gaussian copula assumes perfect correlation in the tails
  3. CCopulas cannot be used when marginal distributions differ
  4. DA Gaussian copula overstates diversification only when correlation is zero

Explanation

The Gaussian copula has asymptotically zero tail dependence, so joint extremes are underweighted relative to the observed clustering in stress. Copulas separate marginals from dependence, so differing marginals are fine. Perfect tail correlation is the opposite of the Gaussian property.

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