FRM Part II · FRM Exam Part II · Credit Scoring and Rating
A one-year transition matrix has states A, B and Default (D, absorbing). From A: A 90%, B 8%, D 2%. From B: A 10%, B 80%, D 10%. Assuming a time-homogeneous Markov process, what is the two-year cumulative default probability for a firm starting in A?
The two-year cumulative default probability is 4.6%. It sums the 2% year-one default, 1.8% from staying in A then defaulting, and 0.8% from moving to B then defaulting. Simply doubling the one-year PD to 4% ignores the higher default risk after migration to B.
- A4.6%Correct
- B2.0%
- C4.0%
- D6.4%
Explanation
Two-year PD = 0.02 (default in year 1) + 0.90*0.02 (stay in A, then default) + 0.08*0.10 (move to B, then default) = 0.02 + 0.018 + 0.008 = 0.046. Check via survival: 0.90*0.98 + 0.08*0.90 = 0.882 + 0.072 = 0.954, so PD is 4.6%. Using 2% twice (4.0%) ignores the migration to B.
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