# Three-state Markov Chain: Credit rating question

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?