mbsconvy

Convexity of mortgage pool given yield

Syntax

Convexity = mbsconvy(Yield,Settle,Maturity,IssueDate,GrossRate)

Convexity = mbsconvy(___,CouponRate,Delay,PrepaySpeed,PrepayMatrix)

Description

Convexity = mbsconvy(Yield,Settle,Maturity,IssueDate,GrossRate) computes mortgage-backed security convexity, given time information, semiannual mortgage yield, and optionally, a prepayment model.

Convexity = mbsconvy(___,CouponRate,Delay,PrepaySpeed,PrepayMatrix) specifies options using one or more optional arguments in addition to the input arguments in the previous syntax.

Examples

Compute the Convexity of a Mortgage Pool Given Yield

This example shows how to compute the convexity of mortgage pool given yield for a mortgage-backed security with the following characteristics.

Yield      = 0.07125;
Settle     = '15-Apr-2002';
Maturity   = '1 Jan 2030';
IssueDate  = '1-Jan-2000';
GrossRate  = 0.08125;
Speed      = 100;
CouponRate = 0.075;
Delay = 14;

Convexity = mbsconvy(Yield, Settle, Maturity, IssueDate, ... 
GrossRate, CouponRate, Delay, Speed)

Convexity = 
72.8263

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

Convexity — Periodic convexity of mortgage pool

scalar numeric

Periodic convexity of mortgage pool, returned as a scalar numeric.

More About

Convexity of Mortgage Pool

The convexity of a mortgage pool refers to the sensitivity of the price of a pool of mortgage-backed securities (MBS) to changes in interest rates, specifically taking into account the nonlinear effects of interest-rate movements over time.

Convexity is a measure of the curvature of the price-yield relationship of a bond or a pool of mortgages, which helps assess how the duration of the asset changes as interest rates change.

References

[1] PSA Uniform Practices, SF-49

Version History

Introduced before R2006a