mbsprice2speed

Implied PSA prepayment speeds given price

Syntax

[ImpSpdOnPrc,ImpSpdOnDur,ImpSpdOnCnv] = mbsprice2speed(Price,Settle,Maturity,IssueDate,GrossRate,PrepayMatrix)

[ImpSpdOnPrc,ImpSpdOnDur,ImpSpdOnCnv] = mbsprice2speed(___,CouponRate,Delay)

Description

[ImpSpdOnPrc,ImpSpdOnDur,ImpSpdOnCnv] = mbsprice2speed(Price,Settle,Maturity,IssueDate,GrossRate,PrepayMatrix) computes PSA prepayment speeds implied by pool prices and projected (user-defined) prepayment vectors. The calculated PSA speed produces the same price, modified duration, or modified convexity, depending upon the output requested.

[ImpSpdOnPrc,ImpSpdOnDur,ImpSpdOnCnv] = mbsprice2speed(___,CouponRate,Delay) specifies options using one or more optional arguments in addition to the input arguments in the previous syntax.

Examples

Compute PSA Prepayment Speeds

This example shows how to compute the equivalent PSA benchmark prepayment speeds for a mortgage pool with the following characteristics and prepayment matrix.

Price        = 101;
Settle       = datetime(2000,1,1);
Maturity     = datetime(2030,1,1);
IssueDate    = datetime(2000,1,1);
GrossRate    = 0.08125;
PrepayMatrix = 0.005*ones(360,1);
CouponRate   = 0.075;
Delay        = 14;

[ImpSpdOnPrc, ImpSpdOnDur, ImpSpdOnCnv] = ... 
mbsprice2speed(Price,Settle, Maturity, IssueDate, ... 
GrossRate, PrepayMatrix, CouponRate, Delay)

ImpSpdOnPrc = 
118.5980

ImpSpdOnDur = 
118.3946

ImpSpdOnCnv = 
109.5115

Input Arguments

Price — Clean price for every $100 face value

vector

Clean price for every $100 face value, specified as an NMBS-by-1 vector.

Data Types: double

Settle — Settlement date

datetime array | string array | date character vector

Settlement date, specified as an NMBS-by-1 vector using a datetime array, string array, or date character vectors. Settle must be earlier than Maturity.

To support existing code, mbsprice2speed also accepts serial date numbers as inputs, but they are not recommended.

Maturity — Maturity date

datetime array | string array | date character vector

Maturity date, specified as an NMBS-by-1 vector using a datetime array, string array, or date character vectors.

To support existing code, mbsprice2speed also accepts serial date numbers as inputs, but they are not recommended.

IssueDate — Issue date

datetime array | string array | date character vector

Issue date, specified as an NMBS-by-1 vector using a datetime array, string array, or date character vectors.

To support existing code, mbsprice2speed also accepts serial date numbers as inputs, but they are not recommended.

GrossRate — Gross coupon rate (including fees)

vector of decimal values

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

Data Types: double

PrepayMatrix — Customized prepayment vector

matrix

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

CouponRate — Net coupon rate

GrossRate (default) | vector of decimal values

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

Data Types: double

Delay — Delay (in days) between payment from homeowner and receipt by bondholder

0 (no delay between payment and receipt) (default) | vector

(Optional) Delay (in days) between payment from homeowner and receipt by bondholder, specified as an NMBS-by-1 vector.

Data Types: double

Output Arguments

ImpSpdOnPrc — Equivalent PSA benchmark prepayment speed for the pass-through to carry the same price

vector

Equivalent PSA benchmark prepayment speed for the pass-through to carry the same price, returned as a NMBS-by-1 vector.

ImpSpdOnDur — Equivalent PSA benchmark prepayment speed for the pass-through to carry the same modified duration

vector

Equivalent PSA benchmark prepayment speed for the pass-through to carry the same modified duration, returned as a NMBS-by-1 vector.

ImpSpdOnCnv — Equivalent PSA benchmark prepayment speed for the pass-through to carry the same modified convexity

vector

Equivalent PSA benchmark prepayment speed for the pass-through to carry the same modified convexity, returned as a NMBS-by-1 vector.

More About

PSA Prepayment Speed

The PSA prepayment speed provides a standardized way to express prepayment rates as a function of time.

The PSA prepayment speed is used to project the rate at which mortgage loans are likely to be paid off early, either through refinancing or selling the property.

References

[1] PSA Uniform Practices, SF-49

Version History

Introduced before R2006a

R2022b: Serial date numbers not recommended

Although mbsprice2speed supports serial date numbers, datetime values are recommended instead. The datetime data type provides flexible date and time formats, storage out to nanosecond precision, and properties to account for time zones and daylight saving time.

To convert serial date numbers or text to datetime values, use the datetime function. For example:

t = datetime(738427.656845093,"ConvertFrom","datenum");
y = year(t)

y =

        2021

There are no plans to remove support for serial date number inputs.