In this paper, we analyze if banks financed with contingent convertible bonds (CoCos) can rely on the classical (CoCo value minimizing) call strategy. Due to further debt positions outstanding, we can show that the optimal (equity value maximizing) call strategy can sharply differ from the simple classical approach. A crucial driver of the optimal call decision is the refinancing assumption of the call price, which determines whether an equal, an early or a late call occurs. In an empirical study comprising 79 European CoCos, we find that the critical stock price triggering a call deviates (on average) by 56.49% from the classical case, which carries over to a CoCo price deviation equal to 8.73%. Our results reveal that the classical call strategy is only justifiable in the special cases of equity injection or junior debt refinancing for a CoCo with a low face value and a late call. Otherwise, the optimal call strategy significantly differs from the classical version and requires knowledge of the particular refinancing assumption.

Agency conflicts and asymmetric information are two possible explanations that may rationalize the use of a step-up provision in the bond indenture. Within a continuous-time framework with bankruptcy costs and tax benefits, we analyze the optimal step-up bond design with respect to both frictions. We find that (i) contrary to existing results, step-up bonds are indeed able to mitigate the asset substitution problem, (ii) the use of a step-up feature can be a credible signal to overcome asymmetric information problems, and (iii) the optimal design as well as the conditions for the optimal use of step-up bonds is considerably different for the two explanations. This outcome implies that, based on observable firm and bond characteristics, it is possible to discriminate between the two motives underlying the use of step-up bonds.