Suppose there are two ratings categories: A and B, along with default. The ratings-migration probabilities look like this for a B-rated loan:
Rating in 1 year Probability
A 0.05
B 0.9
Default 0.05
The yield on A rated loans is 5%; the yield on B rated loans is 10%. All term structures are flat (i.e. forward rates equal spot rates). A loan in default pays off 50%.
a. You have two loans in your portfolio, both are B-rated, 3-year, 10% coupon bonds (paid annually), each with $100 face value. Compute the possible prices of the loans next year in each ratings bucket (just before the first coupon is paid).