Contingent convertible bonds (CCBs) are new debt instruments that automatically convert to equity when the issuing firm or bank reaches a specified level of financial dis- tress. This paper presents a formal model of CCBs with finite maturity and where the firm’s value process is driven by a jump diffusion process. We are able to derive closed- form solutions for the value of the CCBs. In this paper we can completely characterize two different types of CCBs: In the first case the number of shares granted at conversion is fixed a priori. In the second specification the number of shares granted at conversion is chosen a posteriori such that the value of the shares equals a specified value. Incorporating jumps into the dynamics of the firm’s value process is important for two reasons. First it can solve the predictability problem of the conversion and default event, i.e. including jumps into the firm’s value process creates non-zero credit spreads for short maturities. Second, the evaluation of CCBs depends on the capital structure. Without jumps the evaluation of contingent convertible bonds can be independent of the amount of straight debt. In a model with jumps the valuation of straight debt and contingent convertible debt is interlinked as jumps could be large enough to trigger conversion and default simulta- neously. Furthermore, it is observed that short-term debt has very different features than long-term debt. Our model can capture the effect of the maturity on the debt contracts.
In order to apply CCBs in practice it is desirable to base the conversion on observable market prices that can constantly adjust to new information in contrast to accounting trig- gers. We can show how to use credit spreads and the risk premium of credit default swaps to construct the conversion trigger and to evaluate the contracts under this specification.
CCBs are intended to avoid bank bailouts of the type that occurred during the sub- prime mortgage crisis when banks were in trouble to recapitalize themselves and regulators feared the consequences of default contagion. Hence, the second focus of this paper is to analyze whether CCBs can be used as a regulation instrument. It is crucial to require that the parameters of the CCBs are chosen such that they satisfy a no-early-default condition. In this case a regulation that combines a restriction on the maximal leverage ratio and the requirement of issuing a certain fraction of CCBs as part of the whole debt, can efficiently lower the default probability without reducing the total value of the firm. However, if this condition is violated, CCBs can increase the default risk of a bank.