Mortgage Valuation and Optimal Refinancing

Abstract

This paper summarizes recent research on a new approach, namely, an equilibrium approach, to the valuation of fixed-rate mortgage contracts. Working in a discrete time setting, with the mortgagor's prepayment behavior described by a suitable intensity process and with exogenous mortgage rates, the value of the contract is derived in an explicit form that can be interpreted as the value of a certain swap. This leads to a nonlinear equation for what the mortgage rate must be in order to avoid arbitrage opportunities. In other words, endogenous mortgage rates depend upon the mortgagor's prepayment behavior. The complementary problem, where mortgage rates are exogenous and the mortgagor seeks the optimal refinancing strategy, is then solved via a Markov decision chain. Finally, the equilibrium problem, where the mortgagor is a representative agent in the economy who seeks the optimal refinancing strategy and where the mortgage rates are endogenous, is developed and analysed. Existence and uniqueness results, as well as a numerical example, are provided.