Skip to content

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

In a rating-transition model with default as an absorbing state, which statement about the long-run behaviour of the chain is correct, assuming every non-default state can reach default?

The probability of default tends to 1. Default is absorbing and every other state can eventually reach it, so non-default states are transient. Over a long horizon every bond ends up defaulted with probability approaching one.

  1. AThe chain converges to a uniform distribution over all ratings
  2. BThe probability of being in default tends to 1 as time increasesCorrect
  3. CThe probability of being in the highest rating tends to 1
  4. DThe chain has a stationary distribution spread over all non-default states
  5. Default probability stays constant after the first year

Explanation

Default is absorbing, so once entered it is never left. If every other state can reach default, those states are transient, and the probability of being in any of them tends to zero. Hence the only stationary distribution puts all mass on default.

Did you get it right without looking?

One question tells you little. A timed set on Simple models for credit risk shows your real accuracy, how long you take and where you lose marks.

Practise Simple models for credit riskFree diagnostic mock

More Simple models for credit risk questions