Optimal Mortgage Refinancing with Endogenous Mortgage Rates: an Intensity Based, Equilibrium Approach

is that, in practice, mortgagors might be too hasty to refinance just because mortgage rates have dropped. In practice mortgagors probably focus on their

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Optimal Mortgage Refinancing with Endogenous Mortgage Rates: an Intensity Based, Equilibrium Approach
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 principal balance plus the value of a certain swap. This leads to a nonlinear equation for what the mortgage rate must be in a competitive market, and thus mortgage rates are endogenous and 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, solved, and analysed. Existence and uniqueness results, as well as a numerical example, are provided.

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