cmoseqcf

Generate cash flows for sequential collateralized mortgage obligation (CMO)

Syntax

[Balance,Principal,Interest] = cmoseqcf(PrincipalPayments,TranchePrincipalsTrancheCoupons)

[Balance,Principal,Interest] = cmoseqcf(___,HasZ)

Description

[Balance,Principal,Interest] = cmoseqcf(PrincipalPayments,TranchePrincipalsTrancheCoupons) generates cash flows for a sequential CMO without a Z-bond, given the underlying mortgage pool payments.

[Balance,Principal,Interest] = cmoseqcf(___,HasZ) generates cash flows for a sequential CMO with a Z-bond, given the underlying mortgage pool payments, by adding an additional optional input for HasZ.

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 = 1×6
105 ×

    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 = 2×6
105 ×

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

Principal = 2×6
105 ×

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

Interest = 2×6
103 ×

    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