Problem $1$

A fixed$-$income trader observes a three$-$year, $6\mathrm{.}80\%$ annual$-$pay corporate bond trading at $104\mathrm{.}805$ per $100$ of par value. The research team at the hedge fund determines that the riskneutral annual probability of default is $1\mathrm{.}4\%$ and the recovery rate to be applied each year is $25\%.$ The government bond yield curve is flat at $3\mathrm{.}80\%.$

a$.$ Based on these assumptions, does the trader deem the corporate bond to be overvalued or undervalued? By how much?

$($To do this question you will need to calculate the risk$-$free value of the bond, and then the CVA as shown below.$)$

$\backslash$table$[[\backslash$table$[[$Time$],[($years$)]],$Exposure,Recovery,$\backslash$table$[[$Loss Given$],[$Default$]],\backslash$table$[[$Probability of$],[$Default$]],\backslash$table$[[$Probability of$],[$Survival$]],$Expected Loss,$\backslash$table$[[$Discount$],[$Factor $($@ $r_1)]],\backslash$table$[[$PV of$],[$Expected Loss$]]],[1,,,,,,,,],[2,,,,,,,,],[3,,,,,,,,]]$

b$.$ How does the yield spread of the bond compare to its theoretical spread?