Consider a credit rating system consisting of three credit states, A, B and D (default) with the following annual credit transition probability: T = [0.7 0.2 0.1;0.2 0.5 0.3; 0 0 1].
For a company rated B, calculate: a) The credit spread, calculated semi-annually, ten years into the future.
The semi-annually is throwing me off. I know that credit spread = - ln q where q is the solvency. For ten years into the future, we simply take T^10 and the solvency is just 1-default. But they want the credit spread calculated semiannually, ten years into the future.
Edit: I'm wondering if it's asking two different questions ie. calculate credit spread semiannually (T^1/2) and ten years into the future (T^10), or is there a way to calculate the semi annual rate ten years into the future?