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

Two firms, A and B, each have a one-year default probability of 10%. The one-year joint default probability is 3%. What is the one-year default correlation between A and B (binomial default indicators)?

The default correlation is 0.222. Covariance is the joint default probability 0.03 minus the product of the marginals 0.01, giving 0.02, and dividing by the binomial variance 0.09 (0.10 times 0.90) yields 0.222.

  1. A0.200
  2. B0.333
  3. C0.222Correct
  4. D0.030

Explanation

Covariance = 0.03 - 0.10*0.10 = 0.02. Variance of each = 0.10*0.90 = 0.09. Correlation = 0.02/0.09 = 0.222. The 0.200 comes from dividing by 0.10 (using the PD instead of the variance); 0.333 results from dividing 0.03 by 0.09.

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