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FRM Part II · FRM Exam Part II · Estimating Default Probabilities

A simple three-state annual transition matrix has states A, B and D (default). From A: 90% stay in A, 8% move to B, 2% default. From B: 10% move to A, 80% stay in B, 10% default. D is absorbing. What is the two-year cumulative default probability for a bond currently rated B, assuming a time-homogeneous Markov process?

The two-year default probability from B is 0.10 times 2% plus 0.80 times 10% plus the 10% first-year default, which equals 18.2%.

  1. A10.0%
  2. B19.0%Correct
  3. C20.0%
  4. D18.0%

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. Check: 0.182 is 18.2%, so recompute options: nearest listed correct value must be 18.2%, which is not offered, so the question key is invalid.

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