IAI Actuarial Core Principles · Economic Modelling · Simple models for credit risk
A continuous-time Markov model for credit ratings uses a generator matrix with off-diagonal entries equal to transition intensities. A bond rated A has intensity 0.05 to B and 0.01 to default D, and no other moves. What is the expected time the bond stays in rating A before its first move?
The holding time in A is exponential with rate equal to the total exit intensity, 0.05 plus 0.01, which is 0.06. The mean is 1 divided by 0.06, about 16.7 years.
- A6.0 years
- B16.7 yearsCorrect
- C20 years
- D100 years
- 1.0 year
Explanation
The total exit rate from A is 0.05 + 0.01 = 0.06. Holding time is exponential with mean 1/0.06 = 16.67 years. Using only 0.05 gives 20, a missed-intensity error.
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