Optimal Mortgage Design

Abstract

This paper studies optimal mortgage design. A borrower (a household) with limited liability needs financial support from a lender (a big financial institution) to purchase a home. We characterize the optimal allocation in a continuous time setting in which (i) the borrower s income is volatile and its realization is unobservable to the lender, (ii) the lender has a right to costly foreclose the loan and seize the house, (iii) the borrower s intertemporal consumption preferences are represented by a constant discount factor, (iv) the lender discounts cash ows using a stochastic discount factor that depends on the market interest rate. We show that the optimal allocation can be implemented using either a combination of an interest only mortgage with a home equity line of credit or an option adjustable rate mortgage. Under the optimal contracts, mortgage payments and default rates are higher when the market interest rate is high. However, borrowers benefit from low mortgage payments and low default rates when the market interest rate is low. Thus, our analysis provides theoretical evidence that these alternative mortgages, which have recently generated great controversy, can benefit both lenders and borrowers.