FRM Part I · FRM Exam Part I · External and Internal Credit Ratings
A one-year transition matrix has three states: A, B, and D (default, absorbing). From A: A 0.90, B 0.08, D 0.02. From B: A 0.10, B 0.80, D 0.10. Assuming a time-homogeneous Markov chain, what is the two-year cumulative default probability for an issuer currently rated A?
The two-year cumulative default probability is 4.6%. It sums year-one default of 2%, staying in A then defaulting (0.90×0.02=1.8%), and moving to B then defaulting (0.08×0.10=0.8%). Omitting any path gives an incorrect figure.
- A0.0400
- B0.0360
- C0.0260
- D0.0460Correct
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. Doubling 0.02 gives 0.04, which omits the migration paths. The 0.0260 option omits the first-year default of 0.02 (sum of 0.018+0.008).
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