Fixed-Income Toolbox™

mbsyield2oas - Option-adjusted spread given yield

Syntax

OAS = mbsyield2oas(ZeroCurve, Yield, 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. Values are 1 (annual), 2 (semiannual, 3 (three times per year), 4 (quarterly), 6 (bimonthly), 12 (monthly), and -1 (continuous).
`Yield`	Mortgage yield, compounded monthly (in decimal).
`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

OAS = mbsyield2oas(ZeroCurve, Yield, Settle, Maturity, IssueDate, GrossRate, CouponRate, Delay, Interpolation, PrepaySpeed, PrepayMatrix) computes the option-adjusted spread in basis points.

Examples

Calculate the option-adjusted spread of a 30-year, fixed-rate mortgage pool with about 28-year weighted average maturity left, given assumptions of 0, 50, and 100 PSA prepayments.

Create a 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.

Price         = 95;
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 yield, and from the yield, compute the option-adjusted spread.

[mbsyld, beyld] = mbsyield(Price, Settle, ...
Maturity, IssueDate, GrossRate, CouponRate, Delay, PrepaySpeed);

OAS = mbsyield2oas(ZeroCurve, mbsyld, Settle, ...
Maturity, IssueDate, GrossRate, CouponRate, Delay, ... 
Interpolation, PrepaySpeed)

OAS =

   26.0502
   28.6348
   31.2222

mbsyield2oas - Option-adjusted spread given yield

Syntax

Arguments

Description

Examples

See Also