Seller Swap Model
One party sells mortgage pools on its balance sheet and pays the bond interest by entering into a pay-fixed swap with CHT, and receives the interest from MBS pool sold to CHT. This is a seller swap.
Seller Swap Valuation
One party sells mortgage pools on its balance sheet and pays the bond interest by entering into a pay-fixed swap with CHT, and receives the interest from MBS pool sold to CHT. This is a seller swap. The fixed leg is semi annual, and the float leg, MBS coupons, is monthly. In addition, the MBS sold to the trust generates principal cash flows. CHT buys new-pooled mortgages from the party with this principal flows every month until the maturity of the swap.
CHT sold bullet bonds of total notional N that pays C% semi annual coupon for 60 months to investors for P dollars. Using these proceedings, CHT bought a mortgage pool, whose dollar price was P, from the party and entered into a “seller swap” with the party. CHT will buy new mortgage pools from the principal payments generated from the mortgage pools that already bought from the party
The party agreed to pay CHT the coupon of the bond, 
dollars every six months for 5 years. On the floating side, CHT agreed to pay, monthly, all the coupons generated by the mortgage pools it bought from the party for 60 months.
Let 
denotes the first day of month i, for 
assuming 
is the inception of the swap and 
denotes the coupon the party receive at time 
for 
Furthermore, let 
and 
denote the time 
dollar price and unit price of one dollar of notional, respectively of the mortgage pool, 
sold to CHT at time 
Moreover, assume the valuation date t belongs to 
, where m is an integer between 1 and 60. Then
The fair value of the Seller-Swap 
where 
is time t price of a zero coupon bond that matures at time and 
is the price of one dollar notional of the bond at inception.
The time t price of the fixed leg, which includes the notional at maturity, is time t price of the bond less present value of the notional, N.
We show that the time t value of the float- leg is equal to the sum of time t dollar prices of the mortgages the party sold to CHT less expected discounted value of mortgages at the maturity of the swap.
Let 
and 
denotes the time price and notional of all the mortgages the party sold to CHT up to and including time for 
respectively.
At inception, , the party sold one MBS, 
to CHT.
Evolution of 
time dollar Price of :
measurable at time
Coupon for the first month: 
measurable at time
Then 
and 
Principal payment at time 
: 
measurable at time
time dollar Price of : 
measurable at time
Coupon for the second month: 
measurable at time
At time the party received 
and sold another MBS, 
to CHT. i.e.,
where 
is the time price of 
Additionally, we note that
and 
where 
is the time price of 
per one dollar of notional. Table 1 describes the evolution of and during the second month.
Table 1
time price 
Coupon for month 2 
Prepay at time 
time price 
Here, we observe that the first two rows, time price and Coupon for month 2, are measurable at time , and the last two rows, Prepay at time and time price respectively, are measurable at time . The Coupon 
the party received at time 
in dollars is given by
At time , i.e., beginning of the third month, the party received 
amount of cash and sold another MBS, 
to CHT. We note that
and 
where 
is the time price of 
and 
is the time price of per one dollar of notional.
Table 2 describes the evolution of and during the third month.
Table 2
Price at time 
Coupon for month 3 
Prepay at time 
Price at time 
Here, we note that the dollar price of at time , 
is equal to and 
the Coupon the party received at time 
is given by
References:
https://finpricing.com/lib/IrCurve.html
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