Fixed-Income Toolbox™

mbsprice - Mortgage-backed security price given yield

Syntax

[Price, AccrInt] = mbsprice(Yield, Settle, Maturity, IssueDate, 
GrossRate, CouponRate, Delay, PrepaySpeed, PrepayMatrix)

Arguments

`Yield`	Mortgage yield, compounded monthly (in decimal).
`Settle`	Settlement date. A serial date number or date string. `Settle` must be earlier than or equal to `Maturity`.
`Maturity`	Maturity date. A serial date number or date string.
`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.
`PrepaySpeed`	(Optional) Relation of the conditional payment rate (CPR) to the benchmark model. Default = 0 (no prepayment). 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

[Price, AccrInt] = mbsprice(Yield, Settle, Maturity, IssueDate, GrossRate, CouponRate, Delay, PrepaySpeed, PrepayMatrix) computes a mortgage-backed security price, given time information, mortgage yield at settlement, and optionally, a prepayment model.

All outputs are scalar values.

Price is the clean price for every $100 face value of the securities.

AccrInt is the accrued interest of the mortgage-backed securities.

Examples

Example 1. Given a mortgage-backed security with the following characteristics, compute the price and the accrued interest due on the security.

Yield = 0.0725;
Settle = datenum('15-Apr-2002');
Maturity = datenum('1 Jan 2030');
IssueDate = datenum('1-Jan-2000');
GrossRate = 0.08125;
CouponRate = 0.075;
Delay = 14;
Speed = 100;

[Price AccrInt] = mbsprice(Yield, Settle, Maturity, IssueDate,... 
GrossRate, CouponRate, Delay, Speed)

Price =

  101.3147


AccrInt =

    0.2917

Example 2. Given a portfolio of mortgage-backed securities, compute the clean prices and accrued interest.

Yield = 0.075;
Settle = datenum(['13-Feb-2000';'17-Apr-2002';'17-May-2002';... 
'13-Jan-2000']);
Maturity  = datenum('1-Jan-2030');
IssueDate = datenum('1-Jan-2000');
GrossRate = 0.08125;
CouponRate = [0.075; 0.07875; 0.0775; 0.08125];
Delay = 14;
Speed = 100;

[Price AccrInt] = mbsprice(Yield, Settle, Maturity, IssueDate,... 
GrossRate, CouponRate, Delay, Speed)

Price =

   99.7085
  102.0678
  101.2792
  104.0175

AccrInt =

    0.2500
    0.3500
    0.3444
    0.2708

References