Valuation at Origination of Legal Prepayment Options Embedded in 15-Year German Mortgage Loans

Section 489 of the German Civil Code anchors a prepayment option in all fixed-rate retail loans with a term of more than 10.5 years. The primary purpose of this paper is to develop an approach for valuing legal prepayment options (LPOs), embedded in 15-year German mortgage loans, at their origination. The analysis is based on 11,201 pairs of 10-and 15-year German mortgage rates that cover the period from June 2001 until February 2018 in steps of one month. In order to value the LPOs, trajectories of 10-year German mortgage rates are simulated by means of the exponential Vasicek model. The exercise strategy of the borrowers is a main driver of the value of LPOs. Our simulation results reveal that the following exercise strategy maximizes the average value of the LPOs under investigation (from the perspective of the day of their origination): On average, borrowers should exercise their LPOs, embedded in 15-year German mortgage loans, and refinance either if the present value of interest savings is at least 1.2 % of the outstanding loan amount or if the prevailing refinancing rate is, first, below the 15-year mortgage rate and, second, close to its presumed floor of 0.1 %.