IAI Actuarial Core Principles · Economic Modelling · Simple models for credit risk
A one-year transition matrix has states A, B and D (D absorbing). From A: A 0.90, B 0.08, D 0.02. From B: A 0.10, B 0.80, D 0.10. What is the probability that a bond now rated B is in state A after two years?
The probability is 0.17. Sum the two-step paths from B to A: via A gives 0.09, via B gives 0.08, and via default gives zero because default is absorbing.
- A0.170Correct
- B0.100
- C0.080
- D0.640
- 0.180
Explanation
Paths from B to A in two steps: B→A→A = 0.10×0.90 = 0.09; B→B→A = 0.80×0.10 = 0.08; B→D→A = 0. Sum = 0.17. The option 0.18 wrongly adds a path through default, and 0.64 is just the probability of staying in B twice.
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