Pricing the Dynamic Incentive Effects of Contingent Capital

We propose a dynamic continuous-time model that can price and quantify the incentive effects of Contingent Capital (CoCo) bonds which are debt instruments that automatically convert to equity when the issuing bank's capital falls below a pre-defined trigger. We will quantify the argument that if properly designed, CoCo bonds in the capital structure can encourage the bank to keep its capital ratio at higher level and raise equity capital to avoid an automatic conversion to equity. As such, CoCo’s can be potentially a valuable tool for helping bank regulators address the "too big to fail" problem. And a tranche of CoCo bonds in the bank's capital structure can be considered an ex-ante "commitment mechanism" since it can provide the bank with incentives to maintain a more conservative leverage ratio. Our model will provide other important implications for the optimal design of CoCo bonds. For example, the CoCo's that simply writes-down of its principal (like a loss-absorbing bond recently issued by Rabobank that assumes 75% of write-down at the trigger) but not dilute shareholders equity can create perverse incentives that increase the expected cost of financial distress. If the bank becomes distressed and its capital ratio is just above the trigger, the bank may find it optimal to "burn money" (or, equivalently, "burn capital" or "burn assets") to push its capital ratio below the trigger. By burning some amount of assets, the bank can breach the trigger, write-down part of its principal and guarantee a windfall for shareholders. The model will show that the option to "burn money" is likely be in-the-money in times of crisis, when the bank is in financial distress. As suggestion to the financial regulators and policy makers, we demonstrate that the write-down feature of the CoCo bond can be thus highly undesirable, because it is exactly during the crisis that is important to have incentive structures in place that discourage banks from exercising value-destroying strategies. These incentives structures, whether value-creating or value destroying, are not fully understood in the literature on pricing CoCos. The fundamental distinction of our model relative to existing pricing models is the assumption that banks can endogenously raise equity capital to de-lever and reduce the likelihood of CoCo conversion, or to burn money to force the trigger. We will also consider a number of important variations on the model. First, we allow for "jumps" in assets values (i.e., bank runs). In addition, we will quantify conflicts of interest that arise between contingent capital holders, equity holders, and various classes of bond investors. Finally, we will consider the consequence of transaction costs for equity issuance. The structure of the model will be related to the model in Titman and Tsyplakov (2008), which we are attaching. We will be using the numerical algorithm to compute the values of equity and debt which is based on the finite-difference method augmented by a "policy iteration", similar to the algorithm used in Titman and Tsyplakov (2007). Related Paper Sheridan Titman and Sergey Tsyplakov, 2007, "A Dynamic Model of Optimal Capital Structure", Review of Finance, 11: 401-451.