FRM Part I · FRM Exam Part I · Measuring Credit Risk
A one-year transition matrix gives the following for a BBB obligor: 90% stay BBB, 6% move to BB, 4% default. A BB obligor has 85% stay BB, 5% upgrade to BBB, 10% default. Assuming the matrix is time-homogeneous and Markov, with only these three states relevant for the paths (default is absorbing), what is the two-year cumulative default probability for a BBB obligor?
The two-year cumulative default probability is 8.2%, which is not listed.
- A8.0%
- B7.6%
- C8.4%Correct
- D8.8%
Explanation
Year 1 default is 4%. Survivors: 90% at BBB and 6% at BB. Year 2 default = 0.90×4% + 0.06×10% = 3.6% + 0.6% = 4.2%. Cumulative = 4% + 4.2% = 8.2%. Hmm, the BBB row sums to 100% (90+6+4), so the cumulative default probability is 8.2%.
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