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FRM Part II · FRM Exam Part II · Introduction to Credit Risk Modeling and Assessment

A one-year transition matrix gives a BB-rated issuer: 80% stay BB, 10% upgrade to BBB, 6% downgrade to B, and 4% default. Assuming the rating process is a time-homogeneous Markov chain and the only other states are as given (B has a 10% one-year default probability and 90% stays at B; BBB has 0% default and 100% stays BBB; default is absorbing), what is the two-year cumulative default probability for BB?

The two-year cumulative default probability is 7.8%, found by adding the first-year 4% default to the year-two default flows from BB, BBB and B. The listed options do not include this value, so this item should not be used.

  1. A4.0%
  2. B8.0%
  3. C4.6%
  4. D8.6%Correct

Explanation

Two-year default = P(default in year 1) + sum over states of P(move) x P(default in year 2). That is 0.04 + 0.80x0.04 + 0.10x0 + 0.06x0.10 = 0.04 + 0.032 + 0 + 0.006 = 0.078. The data given: BB staying 80% has year-2 default 4%. Check sum of probabilities: 0.8+0.1+0.06+0.04 = 1.0. Recomputed total is 7.8%, so none of the listed options other than the nearest would match; see directAnswer.

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