[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.]

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.

[This article studies optimal mortgage design in a continuous-time setting with volatile and privately observable income, costly foreclosure, and a stochastic market interest rate. We show that the features of the optimal mortgage are consistent with an option adjustable-rate mortgage (option ARM). Under the optimal contract, the borrower is given discretion of how much to repay until his balance reaches a certain limit. The default rates and interest rate payment on the mortgage correlate positively with the market interest rate. Gains from using the optimal contract relative to simpler mortgages are the biggest for those who face more income variability, buy pricey houses given their income level, or make little or no down payment. Our model thus may help to explain a high concentration of option ARMs among riskier borrowers.]

This article studies optimal mortgage design in a continuous-time setting with volatile and privately observable income, costly foreclosure, and a stochastic market interest rate. We show that the features of the optimal mortgage are consistent with an option adjustable-rate mortgage (option ARM). Under the optimal contract, the borrower is given discretion of how much to repay until his balance reaches a certain limit. The default rates and interest rate payment on the mortgage correlate positively with the market interest rate. Gains from using the optimal contract relative to simpler mortgages are the biggest for those who face more income variability, buy pricey houses given their income level, or make little or no down payment. Our model thus may help to explain a high concentration of option ARMs among riskier borrowers.

This paper provides a theoretical analysis of the efficiency of prepayment penalties in a dynamic competitive lending model with risky borrowers and costly default. When considering improvements in the borrower's creditworthiness as one of the reasons for refinancing mortgages, we show that refinancing penalties can be welfare improving and that they can be particularly beneficial to riskier borrowers in the form of lower mortgage rates, reduced defaults, and increased availability of credit. Thus, a high concentration of prepayment penalties among the riskiest borrowers can be an outcome of efficient equilibrium in a mortgage market. We also provide empirical evidence that is consistent with the key predictions of our model.

[This article studies performance-sensitive debt (PSD), the class of debt obligations whose interest payments depend on some measure of the borrower's performance. We demonstrate that the existence of PSD obligations cannot be explained by the trade-off theory of capital structure, as PSD leads to earlier default and lower equity value compared to fixed-rate debt of the same market value. We show that, consistent with the pecking-order theory, PSD can be used as an inexpensive screening device, and we find empirically that firms choosing PSD loans are more likely to improve their credit ratings than firms choosing fixed-interest loans. We also develop a method to value PSD obligations allowing for general payment profiles and obtain closed-form pricing formulas for step-up bonds and linear PSD.]

We study the effects of PPP loans on business competition. We start by introducing temporary cash subsidies into a model of monopolistic competition with differentiated products and heterogeneous production costs. We test the predictions of our model in a sample of U.S. airport hotels for which we observe daily demand, prices, output, and profits. Consistent with model predictions, less profitable businesses were more likely to apply for PPP loans. Businesses with active PPP loans reduced prices, boosting output and profits relative to non-PPP competitors. Those relative differences were reversed once PPP loans expired. We calculate that, for every dollar of PPP subsidies, PPP hotels earned 72.4 cents in extra profits and non-PPP competitors lost 71.4 cents in aggregate. Our results suggest that the PPP initiative distorted competition, imposing significant costs on businesses that chose to forgo these loans.

We consider the optimal design of mortgage-backed securities (MBS) in a dynamic setting in which a mortgage underwriter with limited liability can engage in costly hidden effort to screen borrowers and can sell loans to investors. We show that (i) the timing of payments to the underwriter is the key incentive mechanism, (ii) the maturity of the optimal contract can be short, and that (iii) bundling mortgages is efficient as it allows investors to learn about underwriter effort more quickly, an information enhancement effect. Finally, we demonstrate that the optimal contract can be closely approximated by the “first loss piece.”

Initial proposals for contingent convertibles (CoCos) envisioned that these bonds would convert to equity when the issuing bank’s stock price declined to a prespecified trigger. Subsequent research has claimed that doing so causes the stock price to have multiple equilibria or no equilibrium. We show that when CoCos are perpetuities, which characterizes most actual CoCos, a unique stock price equilibrium exists, except under unrealistic conditions. Unique equilibria occur when conversion favors or disfavors CoCo investors, when CoCos convert to equity or are written down, and when CoCos are callable. We also analyze a bank’s risk choices before and after conversion. Received November 29, 2016; editorial decision July 15, 2018 by Editor Itay Goldstein.

This article studies performance-sensitive debt (PSD), the class of debt obligations whose interest payments depend on some measure of the borrower’s performance. We demonstrate that the existence of PSD obligations cannot be explained by the trade-off theory of capital structure, as PSD leads to earlier default and lower equity value compared to fixed-rate debt of the same market value. We show that, consistent with the pecking-order theory, PSD can be used as an inexpensive screening device, and we find empirically that firms choosing PSD loans are more likely to improve their credit ratings than firms choosing fixed-interest loans. We also develop a method to value PSD obligations allowing for general payment profiles and obtain closed-form pricing formulas for step-up bonds and linear PSD.