We analyze the internal consistency of using the market price of a firm's equity to trigger a contractual change in the firm's capital structure, given that the value of the equity itself depends on the firm's capital structure. Of particular interest is the case of contingent capital for banks, in the form of debt that converts to equity, when conversion is triggered by a decline in the bank's stock price. We analyze the problem of existence and uniqueness of equilibrium values for a firm's liabilities in this context, meaning values consistent with a market‐price trigger. Discrete‐time dynamics allow multiple equilibria. In contrast, we show that the possibility of multiple equilibria can largely be ruled out in continuous time, where the price of the triggering security adjusts in anticipation of breaching the trigger. Our main condition for existence of an equilibrium requires that the consequences of triggering a conversion be consistent with the direction in which the trigger is crossed. For the design of contingent capital with a stock price trigger, this condition may be interpreted to mean that conversion should be disadvantageous to shareholders, and it is satisfied by setting the trigger sufficiently high. Uniqueness follows provided the trigger is sufficiently accessible by all candidate equilibria. We illustrate precise formulations of these conditions with a variety of applications.

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.