# Prepayment Models for Asset-Backed Securities

Because asset-backed security (ABS) yields and maturities depend on an average lifetime rather than a specified lifetime, as is the case with bonds, the accuracy of the projected yields and maturities will depend on accurate projections of prepayments. Projections are based on prepayment models, which, in turn, are based on historical data for the securities of the same or closely related types. Many of these prepayment models are derived from the **PSA model** developed by the Bond Market Association (previously known as the **P**ublic **S**ecurities **A**ssociation; hence, the name of the model).

Because prepayments generally occur when interest rates drop, and because interest rates generally drop slowly, prepayments usually increase in time, then reach a plateau, when the rate of prepayment reaches a steady state. Hence, most prepayment models have an **initial ramp**, when the rate of prepayment increases annually by a certain percentage, then levels off. The duration of the ramp period and the annual percentage increase of the prepayment rate depend on the underlying loan.

Hence, different prepayment models are used with specific assets.

A common metric for mortgage-backed securities is the **single monthly mortality** (**SMM**):

Single Monthly Mortality = Prepayments for the Month / Pool Balance at Beginning of Month

**Constant prepayment rate** (**CPR**) (aka **conditional prepayment rate**), is the compounded percentage of the loan pool that is expected to prepay in the coming year. **Home-equity loans** (**HELs**) and student loans are based on this model.

CPR = Annualized Rate of Monthly Prepayments / Outstanding Balance at Beginning of Period.

The conditional prepayment rate can also be expressed in terms of the single monthly mortality measure:

CPR = 1 - (1 - SMM)^{12}

The **monthly payment rate** (**MPR**) is used for nonamortizing assets, and is calculated according to the following formula:

MPR = (Interest and Principal Payments Received in Month) / Outstanding Balance.

Rating agencies require a minimum MPR for a nonamortizing ABS as an early amortization trigger.

The **absolute prepayment speed** (**APS**) method is used for auto, truck, and RV loans and leases, and is based on the following formula:

APS = Monthly Income / Original Balance

This formula is based on the original balance rather than the outstanding balance because these loans require fixed monthly payments that are a fixed percentage of the original loan. Therefore, if the monthly income drops significantly, this will indicate credit problems with the underlying portfolio and trigger early amortization.

**Prospectus prepayment curve** (aka **pricing prepayment curve**, **PPC**) is a pricing curve used mainly for HELs that is specified in the prospectus for the ABSâ€”hence the name. Since the projected prepayment is specified in the prospectus, the projection varies, and is specific to each ABS issue, depending on the experience of the sponsor or issuer.

**Home-equity prepayment curve** (**HEP**) is also used for HELs. The HEP consists of a 10-month period of even step-ups in the percentage of prepayments per month, starting at 2% in the 1^{st} month, and leveling off at 20% in the 10^{th} month.

**Manufactured-housing prepayment curve** (**MHP**) is a prepayment schedule that is stepped up in the 1^{st} 24 months, starting at 3.7%, with 0.01% increments, then leveling off at 6% in the 24^{th} month. Sometimes an accelerated MHP is used, where 150% or 200% of the percentages are used.