Mortgage Contracts and Underwater Default

SIAM Journal on Financial Mathematics, Volume 15, Issue 2, Page 315-359, June 2024.
Abstract.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 do eliminate selective default, but they 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 an American options pricing methodology, in a continuous-time model with diffusive home prices. The contracts’ values and decision rules are associated with free boundary problems, which admit semiexplicit solutions.