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mbsoas2yield

Yield given option-adjusted spread

Description

example

[MYield,BEMBSYield] = mbsoas2yield(ZeroCurve,OAS,Settle,Maturity,IssueDate,GrossRate) computes the mortgage and bond-equivalent yields of a pass-through security.

example

[MYield,BEMBSYield] = mbsoas2yield(___,CouponRate,Delay,Interpolation,PrepaySpeed,PrepayMatrix) specifies options using one or more optional arguments in addition to the input arguments in the previous syntax.

Examples

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Given an option-adjusted spread, a spot curve, and a prepayment assumption, compute the theoretical yield to maturity of a mortgage pool. First, create the bonds matrix:

Bonds = [datenum('11/21/2002')  0        100  0  2  1;
         datenum('02/20/2003')  0        100  0  2  1;
         datenum('07/31/2004')  0.03     100  2  3  1;
         datenum('08/15/2007')  0.035    100  2  3  1;
         datenum('08/15/2012')  0.04875  100  2  3  1;
         datenum('02/15/2031')  0.05375  100  2  3  1];

Choose a settlement date.

Settle = datenum('20-Aug-2002');

Assume the following clean prices for the bonds:

Prices =  [ 98.97467;
            98.58044;
           100.10534;
            98.18054;
           101.38136;
            99.25411];

Use the following formula to compute spot compounding for the bonds:

SpotCompounding = 2*ones(size(Prices));

Compute the zero curve.

[ZeroRatesP, CurveDatesP] = zbtprice(Bonds, Prices, Settle);
ZeroCurve = [CurveDatesP, ZeroRatesP, SpotCompounding]
ZeroCurve = 6×3
105 ×

    7.3154    0.0000    0.0000
    7.3163    0.0000    0.0000
    7.3216    0.0000    0.0000
    7.3327    0.0000    0.0000
    7.3510    0.0000    0.0000
    7.4185    0.0000    0.0000

Assign the following parameters:

OAS           = [26.0502; 28.6348; 31.2222];
Maturity      = datenum('02-Jan-2030');
IssueDate     = datenum('02-Jan-2000');
GrossRate     = 0.08125;
CouponRate    = 0.075;
Delay         = 14;
Interpolation = 1;
PrepaySpeed   = [0 50 100];

Compute the mortgage yield and bond equivalent mortgage yield.

[MYield BEMBSYield] = mbsoas2yield(ZeroCurve, OAS, Settle, ...
Maturity, IssueDate, GrossRate, CouponRate, Delay, ... 
Interpolation, PrepaySpeed)
MYield = 3×1

    0.0527
    0.0513
    0.0499

BEMBSYield = 3×1

    0.0533
    0.0518
    0.0504

Input Arguments

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Zero curve, specified as a three-column matrix, where:

  • Column 1 is serial date numbers.

  • Column 2 is spot rates with maturities corresponding to the dates in Column 1, in decimal (for example, 0.075).

  • Column 3 is the compounding value of the rates in Column 2. (This is the agency spot rate on the settlement date.) Allowable compounding values are: 1 (annual), 2 (semiannual, 3 (three times per year), 4 (quarterly), 6 (bimonthly), 12 (monthly), and -1 (continuous).

For example:

[datenum('1-Jan-2003')  0.0154  12;
 datenum('1-Jan-2004')  0.0250  12;
 ......
 datenum('1-Jan-2020')  0.0675   2];
 

Data Types: double | char | cell

Option-adjusted spreads, in basis points, specified as an NMBS-by-1 vector.

Data Types: double

Settlement date, specified as an NMBS-by-1 vector using serial date numbers or a cell array of date character vectors. Settle must be earlier than Maturity.

Data Types: double | char | cell

Maturity date, specified as an NMBS-by-1 vector using serial date numbers or a cell array of date character vectors.

Data Types: double | char | cell

Issue date, specified as an NMBS-by-1 vector using serial date numbers or a cell array of date character vectors.

Data Types: double | char | cell

Gross coupon rate (including fees), specified as an NMBS-by-1 vector of decimal values.

Data Types: double

(Optional) Net coupon rate, specified as an NMBS-by-1 vector of decimal values.

Data Types: double

(Optional) Delay (in days) between payment from homeowner and receipt by bondholder, specified as an NMBS-by-1 vector.

Data Types: double

(Optional) Interpolation method to compute the corresponding spot rates for the bond's cash flow, specified as an NMBS-by-1 vector. Available methods are (0) nearest, (1) linear, and (2) cubic spline. For more information on the supported interpolation methods, see interp1.

Data Types: double

(Optional) Speed relative to PSA standard, specified as an NMBS-by-1 vector. The PSA standard is 100.

Note

Set the PrepaySpeed to [] if you input a customized PrepayMatrix.

Data Types: double

(Optional) Customized prepayment vector, specified as a NaN-padded matrix of size max(TermRemaining)-by-NMBS. Each column corresponds to each mortgage-backed security, and each row corresponds to each month after settlement.

Note

Use PrepayMatrix only when PrepaySpeed is unspecified.

Data Types: double

Output Arguments

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Yield to maturity of the mortgage-backed security, returned as a NMBS-by-1 vector. This yield is compounded monthly (12 times a year).

Bond equivalent yield of the mortgage-backed security, returned as a NMBS-by-1 vector. This yield is compounded semiannually (two times a year).

References

[1] PSA Uniform Practices, SF-49

Introduced before R2006a