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Abstract
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.
Disclosure statement
No potential conflict of interest was reported by the authors.
Notes
1 We thank the anonymous referee for their suggestion on this extension.
2 In fact, every central bank voluntarily adjusts the prime interest rate according to the economic state or economic growth rate. Therefore, to some extent, a regime switch in the interest rate represents variations in the economic state or growth rates. Some empirical research finds that economic growth contributes to the formation of particular tastes (e.g. Becker Citation1996; Rapoport and Vidal Citation2007). Accordingly, we assume that changes in the interest rate can trigger variations in the time preferences of time-inconsistent individuals.
3 Time-inconsistent preference has also been applied to asset pricing, for example, Luttmer and Mariotti (Citation2003), Liu et al. (Citation2016), among others.
4 Two-state continuous Markov process is widely used to capture the changes in economic states, see Wang, Wang, and Yang (Citation2016) for labor income state.