The Flexible Mortgage: Optimal Financing of a Consumer Durable

Given the recent flood of new mortgage innovations, it is natural to wonder what features a mortgage which is "optimal" from the consumer's point of view might possess. This paper investigates this issue, using optimal control theory to characterize the time profile of mortgage payments (as well as the value of the mortgage) that maximizes an intertemporal utility function. Among other things, the analysis shows that the optimal mortgage payment stream rises over time under reasonable assumptions, highlighting the non-optimality of the standard flat-payment mortgage.