FRM Part II · FRM Exam Part II · Credit Scoring and Rating
A one-year transition matrix has three states: A, B and D (default). From A: A 90%, B 8%, D 2%. From B: A 10%, B 80%, D 10%. D is absorbing. Assuming a time-homogeneous Markov process, what is the two-year cumulative default probability of a bond currently rated A?
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- A4.0%
- B5.8%Correct
- C3.8%
- D2.0%
Explanation
Two-year PD = P(A→A)·P(A→D) + P(A→B)·P(B→D) + P(A→D)·1 = 0.90×0.02 + 0.08×0.10 + 0.02 = 0.018 + 0.008 + 0.02 = 0.046. Recheck: 0.018+0.008=0.026; 0.026+0.02=0.046, so 4.6%. Therefore none of the listed values would match, so the data must be rechecked: the correct value is 4.6%.
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