Fixed-Income Toolbox™

mbsoas2yield - Yield given option-adjusted spread

Syntax

[MYield, BEMBSYield] = mbsoas2yield(ZeroCurve, OAS, Settle, 
Maturity, IssueDate, GrossRate, CouponRate, Delay, Interpolation, 
PrepaySpeed, PrepayMatrix)

Arguments

`ZeroCurve`	A matrix of three columns: Column 1: Serial date numbers. Column 2: Spot rates with maturities corresponding to the dates in Column 1, in decimal (for example, 0.075). Column 3: Compounding of the rates in Column 2. (This is the agency spot rate on the settlement date.)
`OAS`	Option-adjusted spreads in basis points.
`Settle`	Settlement date (scalar only). A serial date number or date string. Date when option-adjusted spread is calculated.
`Maturity`	Maturity date. Scalar or vector in serial date number or date string format.
`IssueDate`	Issue date. A serial date number or date string.
`GrossRate`	Gross coupon rate (including fees), in decimal.
`CouponRate`	(Optional) Net coupon rate, in decimal. Default = `GrossRate`.
`Delay`	(Optional) Delay (in days) between payment from homeowner and receipt by bondholder. Default = 0 (no delay between payment and receipt).
`Interpolation`	Interpolation method. Computes the corresponding spot rates for the bond's cash flow. Available methods are (0) nearest, (1) linear, and (2) cubic spline. Default = 1. See `interp1` for more information.
`PrepaySpeed`	(Optional) Relation of the conditional payment rate (CPR) to the benchmark model. Default = end of month's CPR. Set `PrepaySpeed` to `[]` if you input a customized prepayment matrix.
`PrepayMatrix`	(Optional) Customized prepayment matrix. A matrix of size `max(TermRemaining)`-by-`NMBS`. Missing values are padded with `NaN`s. Each column corresponds to a mortgage-backed security, and each row corresponds to each month after settlement.

All inputs (except PrepayMatrix) are number of mortgage-backed securities (NMBS) by 1 vectors.

Description

[MYield, BEMBSYield] = mbsoas2yield(ZeroCurve, OAS, Settle, Maturity, IssueDate, GrossRate, CouponRate, Delay, Interpolation, PrepaySpeed, PrepayMatrix) computes the mortgage and bond-equivalent yields of a passthrough security.

MYield is the yield to maturity of the mortgage-backed security (the mortgage yield). This yield is compounded monthly (12 times per year). For example:

0.075 (7.5%)

BEMBSYield is the corresponding bond equivalent yield of the mortgage-backed security. This yield is compounded semiannually (two times per year). For example:

0.0761 (7.61%)

Examples

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

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('08/20/2002');

Assume these clean prices for the bonds.

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

Use this 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];

Assign 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 =

    0.0802
    0.0814
    0.0828

BEMBSYield =

    0.0816
    0.0828
    0.0842

mbsoas2yield - Yield given option-adjusted spread

Syntax

Arguments

Description

Examples

See Also