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Prepayment Models

By Emily Hollis, CFA Partner

Prepayment modeling is a crucial component of analyzing mortgage loans and mortgage-backed securities (MBS) for purposes of investment or ALM analytics. Prepayments by individual mortgage holders affect both the amount and timing of cash flows.

A prepayment model is a stochastic process used to estimate the level of prepayments on a loan portfolio that will occur in a set period of time, given possible changes in interest rates. Sophisticated prepayment models are typically based on mathematical equations derived from the empirical data analysis of historical prepayment trends from large prepayment databases such as FNMA. As interest rates rise, prepayment models factor in fewer prepayments. If interest rates fall, the opposite effect is accounted for, as more people will refinance their loans.

The most simplistic model uses a single prepayment speed for each loan type. As an example, the model will average rates of 30-year, 4.00 percent, fixed-rate mortgages and use a single prepayment speed. This can produce vastly erroneous results, as the propensity of an individual loan to prepay is a function of its specific characteristics.

Other less effective prepayment models aggregate mortgages within ranges of coupons or age that are too wide and then use the relevant prepayment speeds for the average of the band to represent the entire group. For example, 4.00 percent, 30-year-mortgage securities should not have the same prepayment speeds as a portfolio of 3.00 percent and 5.00 percent MBS equally weighted.

But before diving deeper into prepayment models, let’s discuss the definition of prepayment speeds.

Constant prepayment (CPR) and Public Securities Association (PSA) prepayment speeds
CPR is a loan prepayment rate that is equal to the proportion of the principal of a pool of loans that is assumed to be paid off prematurely in each period. Prepayment models are almost entirely driven by full loan refinancing, not curtailments. For example, a pool of mortgages with a CPR rate of 6 percent would indicate that for each period, 6 percent of the pool’s remaining principal outstanding will be paid off in a year’s time.

One of the most notable prepayment models is the PSA Prepayment Model, created by the Securities Industry and Financial Markets Association. The PSA model assumes increasing prepayment rates for the first 30 months and then constant prepayment rates thereafter.

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