Contingent Capital Conversion Under Dual Asset and Equity Jump-Diffusions

We model contingent capital with market trigger under dual jump-diffusion processes in asset values and equity prices. Under the dual jump-diffusions, 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