4. Consider the following one-year transition matrix of credit ratings under the risk-neutral probability:

To

A B Def From

A 0.80 0.20 0

B 0.15 0.75 0.10

Def 0 0 1

1. (i) Compute the (risk-neutral) probability A will default in two years, and the probability B will default in two years.

2. (ii) Suppose that the zero-coupon bonds issued by both A and B have a face value of 1 and that they mature in two years. Further, assume that if these two bonds default, they pay off the same recovery rate, equal to 30%, and only at the end of the second period. Suppose further that the riskless, continuously compounded, the interest rate is r = 2%.

   ii-a Compute the prices of the two bonds. ii-b Compute the credit spreads for the two bonds.