mbsdurp - Duration of mortgage pool given price

Syntax

[YearDuration, ModDuration] = mbsdurp(Price, Settle, Maturity, 
IssueDate, GrossRate, CouponRate, Delay, PrepaySpeed, 
PrepayMatrix)

Arguments

`Price`	Clean price for every $100 face value.
`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] = mbsdurp(Price, Settle, Maturity, IssueDate, GrossRate, CouponRate, Delay, PrepaySpeed, PrepayMatrix) computes the mortgage-backed security Macaulay (YearDuration) and modified (ModDuration) durations, given time information, price at settlement, 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.

Price = 101;
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;

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

YearDuration =

    6.4380

ModDuration =

    6.2080

References

[1] PSA Uniform Practices, SF-49