mbsdury

Duration of mortgage pool given yield

Syntax

[YearDuration,ModDuration] = mbsdury(Yield,Settle,Maturity,IssueDate,GrossRate)

[YearDuration,ModDuration] = mbsdury(___,CouponRate,Delay,PrepaySpeed,PrepayMatrix)

Description

[YearDuration,ModDuration] = mbsdury(Yield,Settle,Maturity,IssueDate,GrossRate) computes the mortgage-backed security Macaulay (YearDuration) in years and modified (ModDuration) durations in years, given time information, yield to maturity, and optionally, a prepayment model.

[YearDuration,ModDuration] = mbsdury(___,CouponRate,Delay,PrepaySpeed,PrepayMatrix) specifies options using one or more optional arguments in addition to the input arguments in the previous syntax.

Examples

Find the Duration of a Mortgage Pool Given the Yield

This example shows how to find the duration of mortgage pool given a mortgage-backed security with the following characteristics.

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

Input Arguments

Yield — Mortgage yield, compounded monthly

vector

Mortgage yield, compounded monthly, specified as an NMBS-by-1 vector in decimals.

Data Types: double

Settle — Settlement dates

vector

Settlement dates, specified as an NMBS-by-1 vector of serial date numbers or a cell array of character vectors. Settle must be earlier than Maturity.

Data Types: double | cell

Maturity — Maturity dates

vector

Maturity dates, specified as an NMBS-by-1 vector of serial date numbers or a cell array of character vectors.

Data Types: double | cell

IssueDate — Issue dates

vector

Maturity dates, specified as an NMBS-by-1 vector of serial date numbers or a cell array of character vectors.

Data Types: double | cell

GrossRate — Gross coupon rate (including fees)

vector

Gross coupon rate (including fees), specified as an NMBS-by-1 vector of numeric decimals.

Data Types: double

CouponRate — Net coupon rate

GrossRate (default) | vector

(Optional) Net coupon rate, specified as an NMBS-by-1 vector of numeric decimals.

Data Types: double

Delay — Delay in days

0 (no delay) (default) | vector

(Optional) Delay in days, specified as an NMBS-by-1 vector.

Data Types: double

PrepaySpeed — Speed relative to PSA standard

0 (no prepayment) (default) | vector

(Optional) Speed relative to PSA standard, specified as an NMBS-by-1 vector. The PSA standard is 100.

Note

Set the PrepaySpeed to [] if you input a customized PrepayMatrix.

Data Types: double

PrepayMatrix — Customized prepayment vector

matrix

(Optional) Customized prepayment vector, specified as 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.

Note

Use PrepayMatrix only when PrepaySpeed is unspecified.

Data Types: double

Output Arguments

YearDuration — Macaulay duration in years

scalar numeric

Macaulay duration in years, returned as a scalar numeric.

ModDuration — Modified duration in years

scalar numeric

Modified duration in years, returned as a scalar numeric.

References

[1] PSA Uniform Practices, SF-49

Version History

Introduced before R2006a