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IAI Actuarial Core Principles · Economic Modelling · Simple models for credit risk

In a Markov chain model of credit ratings with a one-year transition matrix P, which statement best describes the Markov property as applied to a bond's rating?

The Markov property means the distribution of next year's rating depends only on the current rating, not on how the bond arrived there. The relevant row of the transition matrix gives the probabilities, so past rating history adds no information.

  1. AThe next rating depends only on the current rating, not on the path of earlier ratingsCorrect
  2. BThe next rating depends on the time the bond has spent in its current rating
  3. CThe next rating depends on the average of all past ratings
  4. DRatings of different bonds in the same year must be perfectly correlated
  5. Default probability must rise each year the bond survives

Explanation

The Markov property says that, given the present state, the future is independent of the past. So the next-year rating distribution is read from the row of the current rating. The options about time spent in a rating or past averages describe non-Markov (history-dependent) behaviour.

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