A Game-Theoretic Equilibrium Analysis of Fixed-Rate Mortgage with Prepayment Risk

Based on prepayment intensity process, this paper studies the valuation of fixed-rate mortgage contracts and an (game-theoretic) equilibrium model is built. Under the assumption of the rate process of time-homogeneous Markov chain and positive linear refinancing cost, the dynamic programming problem of the mortgagor is simplified to a Markov decision chain with only three discrete state variables which is proved to have a unique solution. The equilibrium is given by a pair of the endogenous rate and the optimal refinancing strategy of the mortgagor. A simple numerical example with an iteration algorithm is finally provided to show how to compute the equilibrium. The results show that the mortgagor is usually too hasty to refinance, thus refinancing is typically a myopic behavior.