  We analyze recently proposed mortgage contracts that aim to eliminate
selective borrower default when the loan balance exceeds the house price (the
``underwater'' effect). We show contracts that automatically reduce the
outstanding balance in the event of house price decline remove the default
incentive, but may induce prepayment in low price states. However, low state
prepayments vanish if the benefit from home ownership is sufficiently high. We
also show that capital gain sharing features, such as prepayment penalties in
high house price states, are ineffective as they virtually eliminate
prepayment. For observed foreclosure costs, we find that contracts with
automatic balance adjustments become preferable to the traditional fixed-rate
contracts at mortgage rate spreads between 20-50 basis points. We obtain these
results for perpetual versions of the contracts using American options pricing
methodology, in a continuous-time model with diffusive home prices. The
contracts' values and optimal decision rules are associated with free boundary
problems, which admit semi-explicit solutions.
