# Credit Spread, Transition Matrix

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?

• Related – Joshua Ulrich Mar 27 '14 at 16:24
• You need a matrix whose square is the annual matrix. The question is covered at quant.stackexchange.com/questions/10645/… – Brian B Mar 30 '14 at 22:44
• Awesome thank you. I finished the question, I'm just wondering now about the yield rate. Id use 1%/2 for the semiannual coupons, yes? – Marie Apr 1 '14 at 1:05