A credit default swap on a $10,000,000, is a two-year agreement, whereby B (the protection buyer) agrees to pay S (the guarantor, or protection seller) a fixed annual fee in exchange for protection against default of two-year bonds XYZ. The payout will be N(100BT)N(100BT), where BTBT is the price of the bond at expiration, if the credit event occurs and NN is the notional. Currently, XYZ bonds are rated A, have recovery rate of 50% and trade at 6.60%. The two-year T-note trades at 6.00%. A simplified transition matrix is shown below.

a. What is the average probability that XYZ bonds will default over a two-year period? (Show work)

\begin{tabular}{ccccc} \hline Start & \multicolumn{4}{c}{ End rating } \\ \cline { 2 - 5 } rating & A & B & C & D \\ \hline A & 0.85 & 0.10 & 0.03 & 0.01 \\ B & 0.05 & 0.90 & 0.03 & 0.02 \\ C & 0.00 & 0.10 & 0.85 & 0.05 \end{tabular} \begin{tabular}{ccccc} \hline Start & \multicolumn{4}{c}{ End rating } \\ \cline { 2 - 5 } rating & A & B & C & D \\ \hline A & 0.85 & 0.10 & 0.03 & 0.01 \\ B & 0.05 & 0.90 & 0.03 & 0.02 \\ C & 0.00 & 0.10 & 0.85 & 0.05 \end{tabular}