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

A risk analyst at a bank models the joint default behavior of 100 corporate borrowers. She specifies each borrower's marginal default probability separately and then uses a Gaussian copula to join them. Which statement best describes the role of the copula in this approach?

A copula joins separately specified marginal distributions into a joint distribution by supplying the dependence structure. The marginals, such as individual default probabilities, are inputs. The Gaussian copula still requires correlations and does not produce tail dependence, which rules out the other statements.

  1. AIt determines each borrower's individual default probability from market prices
  2. BIt links the given marginal distributions into a joint distribution through a dependence structureCorrect
  3. CIt eliminates the need to estimate any correlation parameter
  4. DIt guarantees that tail dependence between defaults is high in stressed markets

Explanation

A copula separates the marginal distributions from the dependence structure. The marginals are specified first, and the copula combines them into a joint distribution. The Gaussian copula still needs correlation inputs and exhibits no tail dependence, so the other statements are wrong.

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