a$.$ What is meant by the term 'credit risk'?

b$.$ What are the key inputs into a model that attempts to quantify credit risk? Explain how each

input would affect credit risk during an economic recession?

c$.$ FM Bank has pooled together $100$ new residential mortgages, each with a loan value of

$200,000.$ The average yield on these mortgages is $8\%.$ FM Bank has sold them to investors

by creating a $3-$tranche Collateralized Debt Obligation $($CDO$).$ Tranche $1$ is the most senior

tranche and accounts for $75\%$ of the total pool and promises to pay investors a yield of $5\%$;

tranche $2($mezzanine$)$ accounts for $20\%$ of the total pool and promises to pay investors a

yield of $10\%$; and tranche $3($junior$)$ accounts for the remainder of the pool and has a

promised yield of $25\%.$

$($i$)$ Why would FM Bank want to create this CDO?

$($ii$)$ Illustrate the structure of the CDO on a diagram

$($iii$)$ If none of the underlying mortgages default, compute the income and profits for FM

bank and the payments that FM bank makes to the investors in the CDO.

$($iv$)$ Following an economic recession, $30\%$ of the mortgages default. Compute the

income and profits for FM bank and the payments that FM bank makes to the investors in the

CDO.