IAI Actuarial Core Principles · Economic Modelling · Simple models for credit risk
In a time-homogeneous Markov rating model, why is default usually treated as an absorbing state?
Default is treated as absorbing because, once an issuer defaults, the model assigns probability 1 to staying in default and zero to moving elsewhere. This simplifies the chain and reflects that recoveries are handled separately.
- ADefaulted issuers are assumed to return to investment grade quickly
- BOnce in default, the issuer's transition probability to remain in default is 1 in the modelCorrect
- CDefault probabilities are always zero for high ratings
- DIt guarantees that the matrix rows sum to less than one
- It makes the chain non-Markov
Explanation
An absorbing state has a self-transition probability of 1, so the issuer never leaves default in the model. Rows still sum to one. The other options contradict this or misstate matrix properties.
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