This paper studies optimal security design in a dynamic setting with an agency problem that arises when an agent in charge of a project can divert cash flows for his own consumption at the expense of an outside investor. Cash flows are unobservable and unverifiable by the outside investor, who relies on the agent's reports, and has the right to liquidate the project. Unlike previous analyses, we allow cash flows to be correlated over time. We solve for the optimal contract and show that it can be implemented using a credit line with an interest rate that increases with the balance on the credit line. This finding is consistent with the fact that the majority of commercial loans are lines of credit with performance pricing. Thus, our model provides theoretical evidence that performance pricing is used to mitigate the agency cost. In addition, we develop a new recursive method to deal with a correlated privately observed variable in dynamic agency settings. It allows us to reduce the dimensionality of the problem and obtain a closed-form solution for the optimal contract.

This paper studies performance-sensitive debt (PSD), the class of debt obligations whose interest payments depend on some measure of the borrower's performance. For example, step-up bonds compensate credit rating downgrades with higher interest rates, and reward credit rating upgrades with lower interest rates. In an endogenous default setting, we propose a method to value PSD obligations allowing for general payment profiles and obtain closed-form pricing formulas in important special cases, including step-up bonds. Moreover, we provide a criterion to compare the efficiency of PSD obligations. In particular, we find that risk-compensating PSD obligations, such as step-up bonds, lead to earlier default and lower equity value compared to fixed-coupon bonds that raise the same amount of cash. Finally, we demonstrate that risk-compensating PSD can be used as a signaling or screening device in a setting with asymmetric information.

This paper studies optimal mortgage design. A borrower (a household) with limited liability needs financial support from a lender (a big financial institution) to purchase a home. We characterize the optimal allocation in a continuous time setting in which (i) the borrower.s income is volatile and its realization is unobservable to the lender, (ii) the lender has a right to costly foreclose the loan and seize the house, (iii) the borrower's intertemporal consumption preferences are represented by a constant discount factor, (iv) the lender discounts cash flows using a stochastic discount factor that depends on the market interest rate. We show that the optimal allocation can be implemented using either a combination of an interest only mortgage with a home equity line of credit or an option adjustable rate mortgage. Under the optimal contracts, mortgage payments and default rates are higher when the market interest rate is high. However, borrowers benefit from low mortgage payments and low default rates when the market interest rate is low. Thus, our analysis provides theoretical evidence that these alternative mortgages, which have recently generated great controversy, can benefit both lenders and borrowers.

We examine the relation between CEOs' equity incentives and their use of performance-sensitive debt contracts. These contracts require higher or lower interest payments when the borrower's performance deteriorates or improves, thereby increasing expected costs of financial distress while also making a firm riskier to the benefit of option holders. We find that managers whose compensation is more sensitive to stock price volatility choose steeper and more convex performance pricing schedules, while those with high delta incentives choose flatter, less convex pricing schedules. Performance pricing contracts therefore seem to provide a channel for managers to increase firms' financial risk to gain private benefits.

Assuming full rationality, we characterize the optimal mortgage contract in a continuous time setting with a risky borrower, costly default, a moral hazard problem between the borrower and the lender, and a stochastic house appreciation. We show that many features of subprime lending observed in practice are consistent with economic efficiency and rationality of both borrowers and lenders. In particular, preferential treatment of risky borrowers is optimal during the housing boom, while default clustering in a group of the most risky borrowers is optimal during the housing slump. We also find that stochastic house appreciation makes it profitable to give loans to risky borrowers who otherwise would be shut out of the housing market, which generates substantial ex-ante utility gains for these borrowers.