In this paper we present compelling evidence froma detailed analysis of historical prepayment datato 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 cohortis a dynamic self-selection process that evolves by itself according tothe encountered mortgage rate environment with the cohort concurrentlyacquiring its memory along the way.
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