Joint Estimation of Baseline Prepayment Function and Prepayment Factor Model of Residential Mortgages Using the Discrete Time Cox Proportional Hazard Model with Stepwise Baseline

We develop a discrete time Cox proportional hazard model with stepwise baseline (DCPHM), a version of the discrete time Cox proportional hazard model, which allows both temporal and cross-sectional variation of prepayment. Unlike the standard Cox proportional hazard model (PHM), which gives the estimates of hazard intensity, DCPHM gives the estimates of conditional prepayment probability directly, which are essential for the valuation of mortgages and mortgage-backed securities. Specifically, DCPHM allows us to estimate the prepayment curve, which is the term structure of conditional prepayment rate (CPR), and prepayment factor model of residential mortgages jointly. Unlike logit, which estimates prepayment factor model only, DCPHM also estimates the baseline prepayment curve. Furthermore, unlike the standard logit model, which only estimates the cross-sectional factor model, DCPHM also estimates the baseline prepayment curve. Joint estimation of baseline prepayment function and prepayment factor model allows us to value mortgages as well as pools of mortgages using the OAS valuation model (Monte Carlo cashflow-based valuation model) directly and efficiently. Using a sample of 145,782 residential mortgages originated in Korea between January 2004 and December 2007, we evaluate the performance of DCPHM in its ability to estimate the term structure of conditional prepayment rate by comparing the baseline prepayment function based on DCPHM and that based on Kaplan-Meyer product limit method. We also evaluate the performance of DCPHM in its ability to estimate the prepayment factor model by comparing estimated factor models based on DCPHM with that based on logit model. We find that the DCPHM estimates both the baseline prepayment function and the prepayment factor model jointly and reliably.