Complete Prepayment Models for Mortgage-Backed Securities

Abstract

The estimation of prepayment rates for pools of mortgages is a critical component in determining the value of mortgage-backed securities—MBS for short—and derivative products. This paper discusses the development of prepayment models for pools of fixed-rate mortgages. The models are complete: calibrated functional forms are given for all of the factors that determine prepayment rates. Hence, the models can be used as benchmarks against the simple models of the Public Securities Association, the Federal Housing Administration experience, or the variety of projected prepayment rates generated by proprietary industry models. The key factors that determine prepayment rates are: (1) refinancing incentive, (2) seasonal variations, (3) seasoning of the mortgage pool, and (4) burnout effect. Each factor is modeled separately and is calibrated using historical data. A multiplicative relationship determines the prepayment rate of the mortgage pool. A novel feature of our model is the use of basis functions that capture the complex interactions between the control variables, i.e., interest rate differentials and time, and the response parameter, i.e., prepayment rates.