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FRM Part II · FRM Exam Part II · Financial Correlation Modeling - Bottom-Up Approaches

A portfolio manager notes that during the credit crisis, defaults clustered far more than a Gaussian copula calibrated to average correlations predicted. Which property of the Gaussian copula most directly explains this shortfall?

The Gaussian copula has no tail dependence, so extreme joint defaults become asymptotically independent however high the correlation. This understates clustering of defaults in crises. The marginals need not be normal, and the standard model uses constant, not stochastic, correlation.

  1. AIt has zero tail dependence, so extreme joint events become asymptotically independentCorrect
  2. BIt requires a different correlation for every pair of names
  3. CIt assumes marginal default probabilities are normally distributed
  4. DIt assumes default correlation is stochastic and mean reverting

Explanation

The Gaussian copula has no tail dependence, so joint extreme outcomes are underestimated relative to observed clustering. Marginals can be any distribution, and the standard model uses constant correlation, not stochastic.

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