# cmoseqcf

Generate cash flows for sequential collateralized mortgage obligation (CMO)

## Syntax

## Description

`[`

generates cash flows for a sequential CMO without a Z-bond, given the underlying
mortgage pool payments.`Balance`

,`Principal`

,`Interest`

] = cmoseqcf(`PrincipalPayments`

,`TranchePrincipals`

`TrancheCoupons`

)

## Examples

### Calculate Cash Flows for a Sequential Collateralized Mortgage Obligation (CMO)

Define the mortgage pool under consideration for CMO structuring using `mbscfamounts`

or `mbspassthrough`

and calculate the cash flows with an A and B tranche for a sequential CMO.

MortgagePrincipal = 1000000; Coupon = 0.12; Terms = 6; % months % Calculate underlying mortgage cash flows [PrincipalBalance, MonthlyPayments, SchedPrincipalPayments, ... InterestPayments, Prepayments] = ... mbspassthrough(MortgagePrincipal, Coupon, Terms, Terms, 0, []); PrincipalPayments = SchedPrincipalPayments.' + Prepayments.'

PrincipalPayments =1×610^{5}× 1.6255 1.6417 1.6582 1.6747 1.6915 1.7084

Define CMO tranches, A and B.

TranchePrincipals = [500000; 500000]; TrancheCoupons = [0.12; 0.12];

Calculate cash flows for each tranche.

```
[Balance, Principal, Interest] = ...
cmoseqcf(PrincipalPayments, TranchePrincipals, TrancheCoupons, false)
```

Balance =2×610^{5}× 3.3745 1.7328 0.0746 0 0 0 5.0000 5.0000 5.0000 3.3999 1.7084 0.0000

Principal =2×610^{5}× 1.6255 1.6417 1.6582 0.0746 0 0 0 0 0 1.6001 1.6915 1.7084

Interest =2×610^{3}× 5.0000 3.3745 1.7328 0.0746 0 0 5.0000 5.0000 5.0000 5.0000 3.3999 1.7084

## Input Arguments

`PrincipalPayments`

— Number of terms remaining for underlying principal payments

numeric matrix

Number of terms remaining for underlying principal payments, specified as
a matrix of size `1`

-by-`NUMTERMS`

, where
`NUMTERMS`

is the number of terms remaining. Each
column contains the underlying principal payment for the time period
corresponding to the row number. Calculate underlying principal payments
using `mbscfamounts`

or
`mbspassthrough`

. The
underlying principal payments can also be outputs from other CMO cash flow
functions.

**Data Types: **`double`

`TranchePrincipals`

— Initial principal for each tranche

numeric matrix

Initial principal for each tranche, specified as a matrix of size
`NUMTRANCHES`

-by-`1`

, where
`NUMTRANCHES`

is the number of tranches in the
sequential CMO. Each element of the matrix represents the initial principal
for each tranche. If the sequential CMO includes a Z-bond
(`HasZ`

is `true`

), the last element
of this matrix is the principal of the Z-bond.

**Data Types: **`double`

`TrancheCoupons`

— Coupon for each tranche

matrix of coupon values

Coupon for each tranche, specified as a matrix of size
`NUMTRANCHES`

-by-`1`

, where
`NUMTRANCHES`

is the number of tranches in the
sequential CMO. Each element of the matrix represents the coupon for each
tranche. If the sequential CMO includes a Z-bond (`HasZ`

is `true`

), the last element of this matrix is the coupon
of the Z-bond. The weighted average coupon for the CMO should not exceed the
coupon of the underlying mortgage.

**Data Types: **`double`

`HasZ`

— Indicates that the sequential CMO contains a Z-bond

`false`

(default) | `true`

| `false`

(Optional) Indicates that the sequential CMO contains a Z-bond, specified
as a Boolean (`true`

or `false`

). A value
of `true`

indicates that the sequential CMO contains a
Z-bond, and the last element of `TranchePrincipals`

and
`TrancheCoupons`

is treated as that of the Z-bond. A
value of `false`

indicates that there is no Z-bond in the
sequential CMO, and the last element of
`TranchePrincipals`

and
`TrancheCoupons`

is treated as an ordinary
tranche.

**Data Types: **`logical`

## Output Arguments

`Balance`

— Principal balance for time period and tranche

matrix

Principal balance for time period and tranche, returned as a matrix of
size `NUMTRANCHES`

-by-`NUMTERMS`

, where
`NUMTRANCHES`

is the number of terms remaining and
`NUMTRANCHES`

is the number of tranches. Each element
represents the principal balance at the time period corresponding to the
column, and for the tranche corresponding to the row.

`Principal`

— Principal payments for time period and tranche

matrix

Principal payments for time period and tranche, returned as a matrix of
size `NUMTRANCHES`

-by-`NUMTERMS`

, where
`NUMTRANCHES`

is the number of terms remaining and
`NUMTRANCHES`

is the number of tranches. Each element
represents the principal payments made at the time period corresponding to
the column, and to the tranche corresponding to the row.

`Interest`

— Interest payments for time period and tranche

matrix

Interest payments for time period and tranche, returned as a matrix of
size `NUMTRANCHES`

-by-`NUMTERMS`

, where
`NUMTRANCHES`

is the number of terms remaining and
`NUMTRANCHES`

is the number of tranches. Each element
represents the interest payments made at the time period corresponding to
the column, and to the tranche corresponding to the row.

## More About

### Sequential Pay CMO

A sequential pay CMO involves tranches that pay off principal sequentially.

For example, consider the following case, where all principal from the underlying mortgage pool is repaid on tranche A first, then tranche B, then tranche C. Interest is paid on each tranche as long as the principal for the tranche has not been retired.

### CMO Tranche

Tranche is a term often used to describe a specific class of bonds within an offering wherein each tranche offers varying degrees of risk to the investor.

## References

[1] Hayre, Lakhbir, ed.
*Salomon Smith Barney Guide to Mortgage-Backed and Asset-Backed
Securities.* John Wiley and Sons, New York, 2001.

[2] Lyuu, Yuh-Dah.
*Financial Engineering and Computation.* Cambridge University
Press, 2004.

## Version History

**Introduced in R2012a**

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