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

A risk manager notes that during the credit crisis, realized default clustering in a CDO portfolio was far greater than that implied by a Gaussian copula calibrated to normal-period correlations. Which is the most appropriate interpretation?

The Gaussian copula has no tail dependence when correlation is below one, so it understates the chance of joint extreme defaults. Empirically correlations also rise in stressed markets, so a copula calibrated in calm periods underestimated default clustering.

  1. AThe Gaussian copula has strong lower tail dependence, so it overstated clustering
  2. BThe Gaussian copula has zero tail dependence for correlations below one, so it understated joint extreme defaults and correlations tend to rise in stressCorrect
  3. CDefault correlation is constant over the cycle, so the shortfall must be due to recovery rates only
  4. DThe Gaussian copula cannot be used with individual default probabilities

Explanation

The Gaussian copula exhibits asymptotic tail independence for correlation below one, so it underestimates joint extreme events. Empirically, default correlations rise in recessions and stress. Option A has the property reversed.

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