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

A structured-credit desk values a CDO tranche using a Gaussian copula with a single flat correlation. Which limitation of this model is most directly relevant to the tranche's pricing during a systemic crisis?

The key limitation is that the Gaussian copula lacks tail dependence, so it understates the likelihood of many simultaneous extreme defaults in a systemic crisis. This tends to underprice the risk of senior tranches, even though the model can be calibrated to tranche prices.

  1. AThe Gaussian copula has no tail dependence, so it understates the probability of joint extreme defaultsCorrect
  2. BThe Gaussian copula requires default times to be exponentially distributed
  3. CThe Gaussian copula cannot be calibrated to any market tranche price
  4. DThe Gaussian copula implies perfect dependence between all obligors

Explanation

The Gaussian copula has zero asymptotic tail dependence, so joint extreme events become unlikely as thresholds go far into the tail, which understates systemic clustering of defaults. It does not require exponential marginals, can be calibrated (giving implied correlation), and does not imply perfect dependence.

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