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

A risk analyst at a bank wants to model the joint distribution of default times for two obligors. She has each obligor's marginal default-time distribution from CDS spreads and wants to combine them into a bivariate distribution using a Gaussian copula. Which statement best describes the role of the copula in this approach?

The copula links already-specified marginal default-time distributions into a joint distribution by imposing a dependence structure, here governed by a correlation parameter. It leaves the marginals unchanged and does not estimate them or make defaults independent.

  1. AIt changes each obligor's marginal default-time distribution to be normal
  2. BIt links the given marginal distributions into a joint distribution through a specified dependence structureCorrect
  3. CIt estimates the marginal default probabilities from market spreads
  4. DIt removes dependence between the obligors so that defaults are independent

Explanation

A copula separates the marginals from the dependence structure. The marginals are taken as given, and the copula (here Gaussian, with a correlation parameter) joins them into a joint distribution. It does not alter the marginals, estimate them, or remove dependence.

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