Contingent Capital Conversion under Jump Diffusions

Abstract

In this paper, we study the design of contingent capital with market trigger under the jump diffusion process. Under the jump diffusion, the issued contingent capital is no longer riskless and has to be priced as a risky junior bond. We find that unique equilibrium requires a very strict condition. Multiple equilibria are expected to be generic. Moreover, even if unique equilibrium condition is satisfied, we show that the conversion ratio is no longer deterministic under the jump diffusion. The conversion ratio becomes a stochastic process related to the jump process of the underlying equity and the conditional expectation of the contingent capital at the conversion time. Thus, making the implementation of contingent capital impossible. The best we can hope to practically implement this conversion design, is to give the minimal conversion ratio (at least the portion required to convert) to conform with Basel III.

Keywords: Banking, Fixed income, Risky bonds, Contingent capital, Equity, Market trigger, Multiple equilibrium, Conversion Policy

JEL Classification: G12, G18, G21, G31