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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Calculate the Principal Balance Schedule for a CMO PAC Bond

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 *

  Columns 1 through 7

    9.7996    9.5780    9.3602    9.1461    8.9357    8.7289    8.5257

  Columns 8 through 14

    8.3259    8.1296    7.9366    7.7469    7.5605    7.3773    7.1972

  Columns 15 through 21

    7.0202    6.8463    6.6754    6.5073    6.3422    6.1799    6.0204

  Columns 22 through 28

    5.8637    5.7096    5.5582    5.4094    5.2632    5.1194    4.9782

  Columns 29 through 35

    4.8394    4.7030    4.5689    4.4372    4.3077    4.1804    4.0554

  Columns 36 through 42

    3.9325    3.8118    3.6931    3.5765    3.4619    3.3494    3.2406

  Columns 43 through 49

    3.1353    3.0334    2.9348    2.8394    2.7470    2.6576    2.5711

  Columns 50 through 56

    2.4873    2.4063    2.3279    2.2520    2.1786    2.1075    2.0387

  Columns 57 through 63

    1.9722    1.9078    1.8455    1.7852    1.7268    1.6703    1.6157

  Columns 64 through 70

    1.5628    1.5117    1.4622    1.4142    1.3679    1.3231    1.2797

  Columns 71 through 77

    1.2377    1.1970    1.1577    1.1197    1.0829    1.0473    1.0129

  Columns 78 through 84

    0.9795    0.9473    0.9161    0.8859    0.8567    0.8285    0.8011

  Columns 85 through 91

    0.7747    0.7491    0.7244    0.7004    0.6773    0.6549    0.6332

  Columns 92 through 98

    0.6122    0.5920    0.5723    0.5534    0.5350    0.5172    0.5001

  Columns 99 through 105

    0.4835    0.4674    0.4518    0.4368    0.4223    0.4082    0.3946

  Columns 106 through 112

    0.3814    0.3687    0.3564    0.3445    0.3330    0.3219    0.3111

  Columns 113 through 119

    0.3007    0.2906    0.2809    0.2715    0.2623    0.2535    0.2450

  Columns 120 through 126

    0.2368    0.2288    0.2211    0.2137    0.2065    0.1995    0.1928

  Columns 127 through 133

    0.1863    0.1800    0.1739    0.1680    0.1623    0.1568    0.1515

  Columns 134 through 140

    0.1464    0.1414    0.1366    0.1319    0.1275    0.1231    0.1189

  Columns 141 through 147

    0.1149    0.1109    0.1072    0.1035    0.0999    0.0965    0.0932

  Columns 148 through 154

    0.0900    0.0869    0.0839    0.0811    0.0783    0.0756    0.0730

  Columns 155 through 161

    0.0704    0.0680    0.0657    0.0634    0.0612    0.0591    0.0570

  Columns 162 through 168

    0.0550    0.0531    0.0513    0.0495    0.0478    0.0461    0.0445

  Columns 169 through 175

    0.0429    0.0414    0.0400    0.0386    0.0372    0.0359    0.0346

  Columns 176 through 182

    0.0334    0.0322    0.0311    0.0300    0.0289    0.0279    0.0269

  Columns 183 through 189

    0.0260    0.0250    0.0241    0.0233    0.0224    0.0216    0.0209

  Columns 190 through 196

    0.0201    0.0194    0.0187    0.0180    0.0174    0.0167    0.0161

  Columns 197 through 203

    0.0155    0.0150    0.0144    0.0139    0.0134    0.0129    0.0124

  Columns 204 through 210

    0.0120    0.0115    0.0111    0.0107    0.0103    0.0099    0.0096

  Columns 211 through 217

    0.0092    0.0089    0.0085    0.0082    0.0079    0.0076    0.0073

  Columns 218 through 224

    0.0070    0.0068    0.0065    0.0063    0.0060    0.0058    0.0056

  Columns 225 through 231

    0.0054    0.0052    0.0050    0.0048    0.0046    0.0044    0.0042

  Columns 232 through 238

    0.0041    0.0039    0.0037    0.0036    0.0035    0.0033    0.0032

  Columns 239 through 245

    0.0031    0.0029    0.0028    0.0027    0.0026    0.0025    0.0024

  Columns 246 through 252

    0.0023    0.0022    0.0021    0.0020    0.0019    0.0018    0.0018

  Columns 253 through 259

    0.0017    0.0016    0.0016    0.0015    0.0014    0.0014    0.0013

  Columns 260 through 266

    0.0012    0.0012    0.0011    0.0011    0.0010    0.0010    0.0009

  Columns 267 through 273

    0.0009    0.0009    0.0008    0.0008    0.0007    0.0007    0.0007

  Columns 274 through 280

    0.0006    0.0006    0.0006    0.0005    0.0005    0.0005    0.0005

  Columns 281 through 287

    0.0004    0.0004    0.0004    0.0004    0.0004    0.0003    0.0003

  Columns 288 through 294

    0.0003    0.0003    0.0003    0.0002    0.0002    0.0002    0.0002

  Columns 295 through 301

    0.0002    0.0002    0.0002    0.0002    0.0001    0.0001    0.0001

  Columns 302 through 308

    0.0001    0.0001    0.0001    0.0001    0.0001    0.0001    0.0001

  Columns 309 through 315

    0.0001    0.0000    0.0000    0.0000    0.0000    0.0000    0.0000

  Columns 316 through 322

    0.0000    0.0000    0.0000         0         0         0         0

  Columns 323 through 325

         0         0         0


InitialBalance =

   100250000

More About

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Planned Amortization Class (PAC) Bond

PAC bonds are a type of CMO bond. They 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.

See Also

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