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FRM Part II · FRM Exam Part II · Credit Scoring and Rating

A one-year transition matrix has three states: A, B and Default (D). 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 for a firm starting in A?

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  1. A4.00%
  2. B5.80%Correct
  3. C3.80%
  4. D9.60%

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. Check: 1 - survival. Survive-year-1 in A 0.90 then survive 0.98 = 0.882; in B 0.08 then survive 0.90 = 0.072; total survival 0.954, so PD = 4.6%. Therefore none of 4.00, 5.80, 3.80 or 9.60 matches, so recompute is required.

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