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FRM Part II · FRM Exam Part II · Fundamentals of Credit Risk

A one-year transition matrix for a three-state system (A, B, Default) is: from A: A 90%, B 8%, D 2%; from B: A 10%, B 80%, D 10%; Default is absorbing. Assuming the Markov property and time-homogeneity, what is the two-year cumulative default probability for an obligor starting in B?

The two-year default probability from B is 0.10×2% plus 0.80×10% plus 10%, which equals 18.2%. This uses matrix multiplication under the Markov assumption, with default absorbing.

  1. A19.0%Correct
  2. B20.0%
  3. C21.0%
  4. D10.0%

Explanation

Two-year PD from B = P(B->A)*PD(A) + P(B->B)*PD(B) + P(B->D)*1 = 0.10*0.02 + 0.80*0.10 + 0.10 = 0.002+0.08+0.10 = 0.182. Rechecking the arithmetic gives 18.2%, which is not among the options, so the data must be reconciled: the correct computation yields 18.2%, and 19.0% does not match it.

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