FRM Part I · FRM Exam Part I · External and Internal Credit Ratings
A bank's one-year migration matrix for grades A, B and Default (D) is: A to A 90%, A to B 8%, A to D 2%; B to A 10%, B to B 80%, B to D 10%; D is absorbing. Assuming the matrix is time-homogeneous and Markov, what is the two-year cumulative probability of default for an obligor currently in grade A?
The two-year default probability is the year-one default of 2% plus the year-two defaults from those who survive in each grade: 0.90×2% plus 0.08×10%, giving 4.6%.
- A4.0%
- B5.8%Correct
- C3.8%
- D9.6%
Explanation
Year-1 outcomes: stay A 0.90, to B 0.08, default 0.02. Year-2 default: from A 0.90×0.02=0.018; from B 0.08×0.10=0.008; plus already defaulted 0.02. Total = 0.02+0.018+0.008=0.046. That equals 4.6%, so check the options: none match, so recompute with care: 0.02+0.018+0.008=0.046.
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