Fixed-Income Toolbox™

mbsdury - Duration of mortgage pool given yield

Syntax

[YearDuration, ModDuration] = mbsdury(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`	Net coupon rate, in decimal. Default = `GrossRate`.
`Delay`	Delay in days.
`PrepaySpeed`	(Optional) Relation of the conditional payment rate (CPR) to the benchmark model. Default = 0. Set `PrepaySpeed` to `[]` if you input a customized prepayment matrix.
`PrepayMatrix`	(Optional) Used only when `PrepaySpeed` is unspecified. Customized prepayment vector. 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.

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

Description

[YearDuration, ModDuration] = mbsdurvy(Yield, Settle, Maturity, IssueDate, GrossRate, CouponRate, Delay, PrepaySpeed, PrepayMatrix) computes the mortgage-backed security Macaulay (YearDuration) and Modified (ModDuration) durations, given time information, yield to maturity, and optionally, a prepayment model.

Note If you specify the PSA or FHA model, it will be seasoned with how long the debt has been outstanding (the loan's age).

Examples

Given a mortgage-backed security with the following characteristics, compute the Macaulay and Modified durations of the security.

Yield = 0.07298413;
Settle = '15-Apr-2002';
Maturity = '1 Jan 2030';
IssueDate = '1-Jan-2000';
GrossRate = 0.08125;
Speed = 100;
CouponRate = 0.075;
Delay = 14;

[YearDuration, ModDuration] = mbsdury(Yield, Settle, Maturity,... 
IssueDate, GrossRate, CouponRate, Delay, Speed)

YearDuration =

    6.4380

ModDuration =

    6.2080

References