FRM Part II · FRM Exam Part II · Structured Credit Risk
Two firms each have a one-year default probability of 10%. The joint default probability is 3%. What is the default correlation (correlation of the default indicator variables)?
The default correlation is 0.222. Covariance equals the 3% joint probability minus 1% (10% times 10%), giving 0.02. Each default indicator has variance 0.09, so the product of standard deviations is 0.09, and 0.02 divided by 0.09 is 0.222.
- A0.222Correct
- B0.300
- C0.111
- D0.020
Explanation
Cov = P(both) - p1*p2 = 0.03 - 0.01 = 0.02. Each variance = 0.10*0.90 = 0.09, so the standard deviation is 0.30 and the product is 0.09. Correlation = 0.02/0.09 = 0.222. The 0.020 option is the covariance only.
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