Optimal mortgage contracts with time-inconsistent preferences

This paper integrates a time-inconsistent preference into the mortgage design problem and studies the corresponding effects on the optimal contract. By assuming exogenous time inconsistency in borrower's preference, we find that the time-inconsistent preference increases the loss in the lender's value and the compensation boundary. We implement the optimal contract using standard securities and option adjustable-rate mortgages (ARMs). The findings show that the time-inconsistent preference increases the default rate, and relative to standard securities, option ARMs increase the total debt capacity, but the borrower's time inconsistency can lead to sudden jumps in the total debt capacity. We also consider the endogenous time inconsistency in the borrower's preference and derive the corresponding mortgage contract; we find that a lender can perfectly offset the effect of a borrower's time inconsistency on the value function and compensation strategy. The liquidation boundary at the low interest rate varies with the degree of time inconsistency, explaining the heterogeneity in mortgage default behaviors observed in practice.