This article develops precise connections among two general approaches to building interest rate models: a general equilibrium approach using a pricing kernel and the Heath, Jarrow, and Morton framework based on specifying forward rate volatilities and the market price of risk. The connections exploit the observation that a pricing kernel is uniquely determined by its drift. Through these connections we provide, for any arbitrage-free term structure model, a representative-consumer real production economy supporting that term structure model in equilibrium. We put particular emphasis on models in which interest rates remain positive. By modeling the dynamics of the drift of the pricing kernel, we construct a new family of Markovian-positive interest rate models.

We study the design and incentive effects of contingent convertible debt. With contingent convertibles, the endogenous bankruptcy boundary can be at either of two levels: one with lower default risk or one at which default precedes conversion. An increase in debt moves the firm from the first regime to the second, a phenomenon we call debt-induced collapse. Setting the conversion trigger sufficiently high avoids this hazard. Given this condition, we investigate the effect of contingent capital and debt maturity on optimal capital structure, debt overhang, and asset substitution. We calibrate the model to large banks during the financial crisis.

This article develops precise connections among two general approaches to building interest rate models: a general equilibrium approach using a pricing kernel and the Heath, Jarrow, and Morton framework based on specifying forward rate volatilities and the market price of risk. The connections exploit the observation that a pricing kernel is uniquely determined by its drift. Through these connections we provide, for any arbitrage-free term structure model, a representative-consumer real production economy supporting that term structure model in equilibrium. We put particular emphasis on models in which interest rates remain positive. By modeling the dynamics of the drift of the pricing kernel, we construct a new family of Markovian-positive interest rate models.

We study the design and incentive effects of contingent convertible debt. With contingent convertibles, the endogenous bankruptcy boundary can be at either of two levels: one with lower default risk or one at which default precedes conversion. An increase in debt moves the firm from the first regime to the second, a phenomenon we call debt-induced collapse. Setting the conversion trigger sufficiently high avoids this hazard. Given this condition, we investigate the effect of contingent capital and debt maturity on optimal capital structure, debt overhang, and asset substitution. We calibrate the model to large banks during the financial crisis. Received April 10, 2015; editorial decision March 20, 2017 by Editor Leonid Kogan.