Consider a credit-rating system, with two solvency states (A & B) and a default state (D), and assuming recovery rate and interest rate are 0%.
- The one year credit spread for an A-rated company is 0.1% and for a B-rated company is 0.22%.
- The two year credit spread for an A-rated company is 0.12% and for a B-rated company is 0.2%.
What is the one-year transition probability matrix?
[My attempt: ]
I used the 1 year credit spreads to obtain the respective elements of the matrix, that is the probabilities of default for both states A & B. So, my one-year transition matrix is as follows:
A B D A x 0.9990005-x 0.0009995 B y 0.9978024-y 0.0021976 D 0 0 1
- How do I use the two year credit spread to obtain the missing values, x & y?
- Am I on the right track?