Many contingent convertible bonds (CoCos) issued since 2014 belong to the additional Tier 1 (AT1) capital of the issuing bank and are thus of a perpetual nature. Within a Black-Scholes setup, under the very conservative assumption that the CoCo trigger is activated by an adverse entity, we are able to derive a closed-form expression for the fair price of such an instrument, provided it has an equity conversion feature (no write-down feature). This formula allows for a quick understanding of the mechanics of such AT1 CoCos, helps to efficiently compute delta-hedge ratios, and it can be implemented easily on a spreadsheet. Furthermore, the closed-form solution may be used as an integral building component of an efficient, semi-analytical pricing formula for AT1 CoCos, when an additional call right for the issuing bank and a step up coupon is present, as typical in the marketplace. Finally, we demonstrate that over the last few years observed CoCo market prices were too high to be explained by our adverse entity assumption, but currently (after the recent Credit Suisse CoCo wipe-out in March 2023) have come down to levels that can be modeled reasonably with our approach. Our approach can therefore be a useful tool to deal with CoCo prices in a market environment with distressed banking sector.
Pricing contingent convertibles with equity conversion feature in a distressed market environment