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FRM Part I · FRM Exam Part I · Measuring Credit Risk

A portfolio manager observes that over a long history, a generator matrix approach is used to build a one-year transition matrix. Which of the following is the primary reason for using a generator matrix rather than raw annual counts when estimating transition probabilities for very rare events such as AAA-to-default?

A generator matrix is used because continuous-time estimation uses all observed migrations and their timing, so rare transitions such as AAA to default receive small positive probabilities, whereas raw annual cohort counts frequently record zero for them.

  1. ARaw counts always overstate default probabilities for investment-grade borrowers
  2. BContinuous-time methods using all observed migrations can give non-zero estimates for rare transitions that raw annual counts show as zeroCorrect
  3. CA generator matrix guarantees that ratings are through-the-cycle
  4. DA generator matrix removes the need to treat default as an absorbing state

Explanation

Cohort counts often show zero for rare transitions like AAA to default over a year. The generator (intensity) approach uses the timing of all migrations, so multi-step paths yield small positive probabilities. It does not change the cycle orientation or the absorbing nature of default.

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