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Mortgage Valuation and Optimal Refinancing, Pliska

An equilibrium valuation of fixed-rate mortgage contracts in
discrete time -- the mortgagor’s prepayment behavior
described by 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.

A nonlinear equation for what the mortgage rate 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.

Mortgage Valuation and Optimal Refinancing, Stanley R. Pliska.

Existence and uniqueness results, as well as a numerical
example, are provided.

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