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FRM Part II · FRM Exam Part II · Structured Credit Risk

A risk manager argues that the Gaussian copula understated senior CDO tranche risk before the 2007-2009 crisis. Which of the following is the most accurate critique of the model as typically applied?

The Gaussian copula has no tail dependence, and a single constant correlation was typically calibrated to calm markets. Real-world default correlations rise in stress, so the model underestimated the probability of many simultaneous defaults and therefore the risk to senior CDO tranches.

  1. AIt has zero tail dependence, and a single constant correlation was calibrated to benign periods, so joint extreme defaults were underestimatedCorrect
  2. BIt assumes default probabilities are perfectly correlated across all obligors, overstating diversification
  3. CIt requires default times to follow a Poisson process with a constant hazard rate, which cannot be changed
  4. DIt produces negative default correlation in stressed markets, lowering senior tranche spreads

Explanation

The Gaussian copula has no asymptotic tail dependence, so joint extreme events are assigned low probability, and correlations estimated in calm markets tend to rise in stress. Together these understate senior tranche losses. Option B is wrong because the model does not assume perfect correlation, and C is wrong because hazard rates can be time-varying.

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