Stochastic House Appreciation and Optimal Mortgage Lending

We characterize the optimal mortgage contract in a continuous time setting with stochastic growth in house price and income, costly foreclosure, and a risky borrower who requires incentives to repay his debt. We show that many features of subprime loans can be consistent with properties of the optimal contract and that, when house prices decline, mortgage modification can create value for borrowers and lenders. Our model provides a number of empirical predictions that relate the features of mortgage contracts originated in a housing boom and the extent of their modification in a slump to location and borrowers' characteristics.