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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)?

Solution for cash flows

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.

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  • $\begingroup$ Please click on the image to have a large view. $\endgroup$ – Silent_bliss Sep 9 '20 at 6:56
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    $\begingroup$ Try excel PMT function: PMT(8.125%/12,357, -400m,,0). $\endgroup$ – Magic is in the chain Sep 9 '20 at 8:00
  • $\begingroup$ @Magicisinthechain it is working in excel. Any idea how to compute it manually? $\endgroup$ – Silent_bliss Sep 9 '20 at 16:07
  • $\begingroup$ Here goes: $\mathrm{pmt}=\frac{r}{12} \frac{\mathrm{PV}}{1-\left(1+\frac{r}{12}\right)^{-n}}$ $\endgroup$ – Magic is in the chain Sep 9 '20 at 16:30
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    $\begingroup$ It is minus n: 1−(1+0.08125÷12)^−357=0.91 $\endgroup$ – Magic is in the chain Sep 9 '20 at 17:38
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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.

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