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 joint one-year default probability of both firms is 4%. What is the one-year default correlation between A and B (Bernoulli default indicators)?
The default correlation is 0.33. The covariance is the joint default probability of 4% minus the product of 10% and 10%, which gives 0.03. Dividing by the variance of each default indicator, 0.09, yields a correlation of one third.
- A0.22
- B0.33Correct
- C0.40
- D0.15
Explanation
Covariance = 0.04 - 0.10*0.10 = 0.03. Variance of each indicator = 0.10*0.90 = 0.09. Correlation = 0.03/0.09 = 0.333. Using 0.04/0.09 = 0.44 or forgetting to subtract the product would be an error; 0.22 comes from dividing 0.02 by 0.09, which is wrong.
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