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cmosched

Generate principal balance schedule for planned amortization class (PAC) or targeted amortization class (TAC) bond

Syntax

[BalanceSchedule,InitialBalance] = cmosched(Principal,Coupon,OriginalTerm,TermRemaining,PrepaySpeed)
[BalanceSchedule,InitialBalance] = cmosched(Principal,Coupon,OriginalTerm,TermRemaining,PrepaySpeed,TranchePrincipal)

Description

[BalanceSchedule,InitialBalance] = cmosched(Principal,Coupon,OriginalTerm,TermRemaining,PrepaySpeed) generates a principal balance schedule for planned amortization class (PAC) bonds using two bands of Public Securities Association Prepayment Model (PSA) speeds or targeted amortization class (TAC) bonds using a single PSA speed.

[BalanceSchedule,InitialBalance] = cmosched(Principal,Coupon,OriginalTerm,TermRemaining,PrepaySpeed,TranchePrincipal) with a specified tranche principal generates a principal balance schedule for planned amortization class (PAC) bonds using two bands of PSA speeds or targeted amortization class (TAC) bonds using a single PSA speed.

Input Arguments

Principal

Principal of the underlying mortgage pool.

Coupon

Coupon of the underlying mortgage pool.

OriginalTerm

Original term in months of the underlying mortgage pool.

TermRemaining

Terms remaining in months of the underlying mortgage pool.

PrepaySpeed

PSA speed. For a PAC, the speed is a 1-by-2 matrix where the first element is the lower band and the second element is the upper band. For a TAC, the speed is a scalar.

TranchePrincipal

(Optional) Principal of the scheduled tranche. If it is unspecified or empty [], the principal of the scheduled tranche is assumed to be the sum of the payment schedule calculated from the PSA prepayment speeds.

Output Arguments

BalanceSchedule

Matrix of size 1-by-NUMTERMS, where NUMTERMS is the number of terms remaining. Each column contains the scheduled principal balance for the time period corr-by-esponding to the column number.

InitialBalance

Scalar containing the initial principal balance of the scheduled tranche.

Examples

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Define the mortgage pool under consideration and generate a principal balance schedule for planned amortization class (PAC) bonds using two bands of PSA speeds.

Principal = 128687000;
GrossRate = 0.0648;
OriginalTerm = 360;
TermRemaining = 325;
PrepaySpeed = [300 525];
PacPrincipal = 100250000;

[BalanceSchedule, InitialBalance] ...
= cmosched(Principal, GrossRate, OriginalTerm, TermRemaining, ...
PrepaySpeed, PacPrincipal)
BalanceSchedule = 

   1.0e+07 *

    9.7996    9.5780    9.3602    9.1461    8.9357    8.7289    8.5257    8.3259    8.1296    7.9366    7.7469    7.5605    7.3773    7.1972    7.0202    6.8463    6.6754    6.5073    6.3422    6.1799    6.0204    5.8637    5.7096    5.5582    5.4094    5.2632    5.1194    4.9782    4.8394    4.7030    4.5689    4.4372    4.3077    4.1804    4.0554    3.9325    3.8118    3.6931    3.5765    3.4619    3.3494    3.2406    3.1353    3.0334    2.9348    2.8394    2.7470    2.6576    2.5711    2.4873

InitialBalance = 100250000

More About

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Planned Amortization Class (PAC) Bond

PAC bonds are a type of CMO bond and are designed to largely eliminate prepayment risk for investors.

They do this by transferring essentially all prepayment risk to other bonds in the CMO that are called support bonds.

Targeted Amortization Class (TAC) Bond

TAC bonds are analogous to PAC bonds, but are structured differently.

TAC bonds offer one-sided protection, shielding investors from high prepayment rates up to a specified PSA and do not protect against low prepayment rates.

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.

Introduced in R2012a

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