OPTIMAL MORTGAGE REFINANCING WITH ENDOGENOUS MORTGAGE RATES

Stanley Pliska

Abstract

This paper builds on work with and by Yevgeny Goncharov, which used an intensity based approach to derive new relationships and results for the value of a mortgage contract that is subject to prepayment risk. In particular, with the prepayment behavior and the riskless interest rate process specified exogenously, it was shown with arbitrage pricing theory that the interest rate for a fixed rate mortgage is an endogenous quantity that can readily be computed. This paper considers the complementary problem: the riskless and mortgage interest rates are specified, and one seeks the optimal refinancing strategy for the mortgagor. Markov decision theory is used to solve this problem in a discrete time context. The paper then addresses the natural equilibrium problem: the mortgagor acts optimally, and the mortgage rate process satisfies a no-arbitrage condition. An example is presented where this equilibrium problem is solved explicitly.