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FRM Part II · FRM Exam Part II · Credit Risk Management

A bank's one-year transition matrix gives a B-rated loan a 10% default probability, and 70% probability of staying B. For an analyst wanting the cumulative default probability over time using the matrix, which feature of default makes repeated multiplication of the matrix appropriate?

Default is modelled as an absorbing state, meaning once an obligor defaults it stays there. Therefore the default column of the matrix raised to the power n gives the cumulative probability of default over n years.

  1. ADefault is an absorbing state, so once reached it is never leftCorrect
  2. BDefault is treated as an upgrade to the highest rating
  3. CDefault has a probability that declines each year
  4. DDefault is excluded from the matrix

Explanation

With default absorbing, the default column of the matrix power gives cumulative default probability since defaulted obligors stay defaulted. The other options misdescribe the matrix.

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