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

During a market stress episode, a risk team observes that default correlations among reference names in a CDO portfolio rise sharply, while the Gaussian copula model calibrated before the stress had assumed stable correlations. Which model limitation does this best illustrate?

This illustrates that the Gaussian copula has no tail dependence and uses a static correlation. It therefore underestimates joint extreme defaults and fails to capture correlations rising in stress, which can leave senior tranches materially mispriced.

  1. AThe Gaussian copula has strong tail dependence, so it overstated joint defaults
  2. BThe Gaussian copula has zero tail dependence and assumes a constant correlation, so it understated joint extreme defaults and ignored correlation instabilityCorrect
  3. CThe model overstated recovery rates only, without any link to correlation
  4. DThe model cannot be applied to portfolios with more than ten names

Explanation

The Gaussian copula lacks tail dependence, so extreme joint defaults are underestimated, and a single constant correlation does not capture correlations rising in stress. The claim of strong tail dependence is wrong since it is the Student t copula that has tail dependence.

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