$($a$)[20$pts$]$ You are considering the purchase of a $$350$ million private label mortgage pass$-$

through security for $104-31.$ It consists of originally $15-$year fixed rate prime mortgages with

WAM $170$ months, WAC $7\%$ and deal coupon $6\mathrm{.}75\%($MEY$).$ Your base case assumption is for a

PSA of $100$ and SDA of $75($see recovery provision below$).$ Amortize the deal and compute the

modified duration, convexity, and static spread, assuming that the PSA and SDA do not change.

Note: $(1)$ assume a Treasury spot rate curve given by $z(T)={0\mathrm{.}03}^{**}ln[0\mathrm{.}025(T+40)],$ where $T$ is

measured in months to maturity and $z$ is an MEY.

$(2)$ You may use the following for the SDA, with appropriately modified cell references:

$(3)$ Default recovery: $35\%$ of defaulted principal is recovered with a $10-$ month lag and

distributed as CF to the pool. This will be counted as a principal cash flow but note that it

does not alter the ending balance in any month.

$($b$)[10$pts$]$ You believe that $13$ months from now, the PSA and SDA could change $($from the base

case in part $($a$)$; so$,$ they stay at base values for $12$ payments, then change$)$ to one of $9$

combinations according to the following probability table:

Compute the mean and standard deviation for the modified duration, convexity, and static

spread.

Note: Copy part $($a$)$ into a new tab $($PartB$)$ before making the necessary alterations. You will

want the What$-$if tables to be at the bottom of this tab's amortization table but transfer the

results $($using $=$cell address$)$ to a new tab called PartB$1$ to perform your calculations.