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

Two assets have marginal default times that are exponential with hazard rates giving 1-year default probabilities of 10% each. Their default times are joined by a Gaussian copula with correlation 0 between the underlying normal variables. What is the probability that both default within one year?

With zero correlation, the Gaussian copula implies independence, so the joint default probability is the product of the marginal probabilities: 10% × 10% = 1%. Adding probabilities gives 20%, and using one marginal alone gives 10%, both of which are incorrect.

  1. A10%
  2. B1%Correct
  3. C0.1%
  4. D20%

Explanation

With zero correlation the Gaussian copula implies independence, so the joint probability is the product of the marginals: 0.10 × 0.10 = 0.01, or 1%. Taking 10% ignores the second asset, and 20% adds rather than multiplies.

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