mbsprice2speed - Implied PSA prepayment speeds given price

Syntax

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

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.
`PrepayMatrix`	Customized prepayment matrix. A matrix of size `max(TermRemaining)`-by-`NMBS`. Missing values are padded with `NaN`s. Each column corresponds to a mortgage-backed security, and each row corresponds to each month after settlement.
`CouponRate`	(Optional) Net coupon rate, in decimal. Default = `GrossRate`.
`Delay`	(Optional) Delay (in days) between payment from homeowner and receipt by bondholder. Default = 0 (no delay between payment and receipt.

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

Description

[ImpSpdOnPrc, ImpSpdOnDur, ImpSpdOnCnv] = mbsprice2speed(Price, Settle, Maturity, IssueDate, GrossRate, PrepayMatrix, CouponRate, Delay) 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 calculates the equivalent PSA benchmark prepayment speed for the pass-through to carry the same price.

ImpSpdOnDur calculates the equivalent PSA benchmark prepayment speed for the pass-through to carry the same modified duration.

ImpSpdOnCnv calculates the equivalent PSA benchmark prepayment speed for the pass-through to carry the same modified convexity.

All outputs are NMBS-by-1 vectors.

Examples

Calculate the equivalent PSA benchmark prepayment speeds for a mortgage pool with these characteristics and prepayment matrix.

Price        = 101;
Settle       = datenum('1-Jan-2000');
Maturity     = datenum('1-Jan-2030');
IssueDate    = datenum('1-Jan-2000');
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

References

[1] PSA Uniform Practices, SF-49