### 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:

shorter and longer versions.

Existence and uniqueness results, as well as a numerical

example, are provided.