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

In a rating-based credit risk model using a transition matrix, which statement is correct?

In a rating transition matrix each row gives the probabilities of moving from a given current rating to every rating, including default, and so sums to one. Default is normally absorbing and the Markov property ignores earlier history.

  1. ADefault is normally modelled as a transient state from which firms can return to the highest rating
  2. BEach row gives probabilities of moving from a given rating to each possible rating over the period and sums to oneCorrect
  3. CEach column of the matrix sums to one
  4. DRating changes are assumed to depend on the full history of previous ratings
  5. The default state is assigned a probability of zero of remaining in default

Explanation

In a Markov transition matrix, row i lists the probabilities of moving from state i to every state, so rows sum to one. Default is usually absorbing, so staying in default has probability one. The Markov assumption means history does not matter beyond the current rating.

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