Calculating Scheduled Payments for a Mortgage Pass-Through Pool
Summary
The document explains how to calculate the scheduled monthly payment for a mortgage pass-through pool using its balance, gross weighted-average coupon, and remaining term. Convert the annual coupon to a monthly rate, then apply the level-payment annuity formula. The example concerns a pool with stated balance, coupon, and maturity and asks how the first month’s scheduled-payment figure was obtained; the response identifies it as the standard payment calculation for a level-payment pool with monthly amortization.
The scheduled payment can change over time as loans with different terms leave the pool and as borrower curtailments reduce the remaining term. The explanation distinguishes this scheduled payment calculation from broader cash-flow estimation, but does not work through the example’s arithmetic or explain the effects of prepayments under the stated PSA assumption. The cited book is offered as further reference, without detail from it.
Key ideas
- Convert the gross weighted-average coupon to a monthly rate before calculating payment.
- The level-payment formula uses the current balance, monthly rate, and remaining term.
- A pool’s scheduled payment may change as loans exit or borrowers make curtailments.
- The answer does not show the numerical substitution for the example.
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Full text
# How to calculate scheduled mortgage payment of a mortgage pass-through security?
# How to calculate scheduled mortgage payment of a mortgage pass-through security?
I am trying to estimate the cash flows of Mortgage Backed Security. The example is present in the Fixed Income textbook written by Fabozzi.
The problem and the solution is as follows:-
Suppose there is a $400 million mortgage pass-through security with a 7.5% pass-through rate, a weighted average coupon of 8.125% and a weighted average maturity of 357 months, how to compute the cash flows for the next two months assuming a 100 Principal Securities Association(PSA)?
I have understood the values for all the columns except for column 5. Could anyone how did the value of $2,975,868 come up in the scheduled mortgage payment for month 1?
Even the text book does not provide any references with respect to this.
## Answer by Sharad (score 2)
https://quant.stackexchange.com/a/58114
As per the answer by Magic is in the chain, this is just the calculation for the standard payment on a level-payment MBS pool with monthly amortization. If $B$ is the balance, $WAC$ is the gross weighted-average coupon (in percent), and $R$ is the remaining term (in months), set $G = WAC/12$ and $U = 1/(1+G)$. The monthly payment is then given by:
$PMT = \frac{B * G}{1-U^R}$
The standard payment keeps changing from month to month because (a) a 30-year MBS pool can have loans with a range of terms in it and the average remaining term of the pool may change as some of these loans exit the pool, and (b) Mortgagors often send in a little more than their scheduled monthly payments and these so-called curtailments act to effectively lower the remaining term of the mortgage.
For details, see "Guide to Mortgage-backed Securities" by Lakhbir Hayre et al.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.