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cmoseqcf

Generate cash flows for sequential collateralized mortgage obligation (CMO)

Syntax

[balances, principals, interests] =
cmoseqcf(PrincipalPayments, TranchePrincipals, TrancheCoupons)
[balances, principals, interests] =
cmoseqcf(PrincipalPayments, TranchePrincipals, TrancheCoupons, HasZ)

Description

[balances, principals, interests] =
cmoseqcf(PrincipalPayments, TranchePrincipals, TrancheCoupons)
generates cash flows for a sequential CMO without a Z-bond, given the underlying mortgage pool payments.

[balances, principals, interests] =
cmoseqcf(PrincipalPayments, TranchePrincipals, TrancheCoupons, HasZ)
generates cash flows for a sequential CMO with a Z-bond, given the underlying mortgage pool payments.

Input Arguments

PrincipalPayments

Matrix of size 1-by-NUMTERMS, where NUMTERMS is the number of terms remaining. Each row contains the underlying principal payment for the time period corresponding to the row number. The underlying principal payments can be calculated using mbscfamounts or mbspassthrough. The underlying principal payments can also be outputs from other CMO cash flow functions

TranchePrincipals

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.

TrancheCoupons

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.

HasZ

(Optional) 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 will be 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 will be treated as an ordinary tranche.

Default: false

Output Arguments

Balance

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

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

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.

Examples

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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 =

   1.0e+05 *

    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 =

   1.0e+05 *

    3.3745    1.7328    0.0746         0         0         0
    5.0000    5.0000    5.0000    3.3999    1.7084    0.0000


Principal =

   1.0e+05 *

    1.6255    1.6417    1.6582    0.0746         0         0
         0         0         0    1.6001    1.6915    1.7084


Interest =

   1.0e+03 *

    5.0000    3.3745    1.7328    0.0746         0         0
    5.0000    5.0000    5.0000    5.0000    3.3999    1.7084

More About

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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. Note that 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

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

Lyuu, Yuh-Dah, Financial Engineering and Computation, Cambridge University Press, 2004.

See Also

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