FRM Part II · FRM Exam Part II · Credit Risk Management
A bank has a one-year transition matrix with states A, B, and Default (absorbing). From A: stay A 90%, to B 8%, default 2%. From B: to A 10%, stay B 80%, default 10%. A loan is currently rated B. What is the probability it is in default at the end of two years?
The two-year default probability is 18.2%: 10% in year one, plus 10%×2% via A, plus 80%×10% via staying in B, giving 0.10+0.002+0.08.
- A10.0%
- B19.0%Correct
- C20.0%
- D21.0%
Explanation
Year-1 default is 10%. Survivors: A with 10% then default 2% gives 0.10×0.02=0.002; stay B 80% then default 10% gives 0.08. Total = 0.10+0.002+0.08=0.182. Recheck gives 18.2%, so none of the listed values matches; the correct figure is 18.2%.
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