[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 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.]

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.

We analyze how Dodd-Frank-mandated risk retention affects the information investors extract from issuers’ retention choices in the CMBS market. We show that the required retention level is both binding and stringent. Although this implies issuers cannot signal using the level of retention, we provide a model showing that signaling can occur by varying the retention structure. The model is consistent with spreads being empirically lower in deals with a purely first-loss retention structure. A stated concern of rulemakers is asymmetric information. However, we show that, post-crisis, the level of asymmetric information in this market is quite low.

We show that commercial mortgage borrowers behave opportunistically to attempt to obtain principal reductions. We develop a model in which lenders cannot perfectly observe borrowers’ use values and renegotiation is costly. We then exploit a tax rule change that reduced the cost of renegotiation. Consistent with the model predictions, borrowers with high private use values of the property are more likely to transfer into special servicing when lenders have a higher capacity to negotiate principal reductions after the rule change. Our results suggest adverse consequences of principal forgiveness for lenders.