Burnout from pools to loans: Modeling refinancing prepayments as a self-selection process

In this paper we present compelling evidence from a detailed analysis of historical prepayment data to demonstrate that a mortgage cohort remembers the level of the previous mortgage rate troughs experienced by the cohort. This is a general property, observed ubiquitously, that inescapably leads to refinancing models with a continuous distribution of refinancing incentive thresholds (elbows). We present such a new refinancing model, derived from the first principle, based on a single assumption that each loan has an incentive threshold above which its borrower will refinance. In this model, the refinancing prepayment of a cohort is a dynamic self-selection process that evolves by itself according to the encountered mortgage rate environment with the cohort concurrently acquiring its memory along the way.