Enhanced equity-credit modelling for contingent convertibles

Abstract

Contingent convertible (CoCo) bonds are characterized by forced equity conversion under either an accounting or regulatory trigger. The accounting trigger occurs when the capital ratio of the issuing bank falls below some contractual threshold. Under the regulatory trigger, sometimes called the point-of-non-viability (PONV) trigger, the regulatory authority may enforce equity conversion when the financial health of the bank deteriorates to certain distressed level. In this paper, we propose an equity-credit modelling of the joint process of the stock price and the capital ratio that integrates both a structural approach for the accounting trigger and a reduced-form approach for the PONV trigger of equity conversion. We also construct effective Fortet algorithms and finite difference schemes for numerical pricing of CoCo bonds under various forms of equity conversion pay-off. The pricing properties of CoCo bonds are examined under different assumptions for the state-dependent intensity of the PONV trigger, the contractual specifications and market conditions.

Keywords:

• Contingent convertibles
• Equity-credit modelling
• Fortet algorithms

Acknowledgements

We appreciate the constructive comments and suggestions from two anonymous referees which significantly contributed to improving the paper. The views and opinions expressed here are those of the authors and do not reflect the views of the Mitsubishi UFJ Trust Investment Technology Institute.

Notes

No potential conflict of interest was reported by the authors.

1 We ignore the small amount of interest accrual when a conversion occurs between two consecutive coupon payment dates.

2 We apply the CDS analogy here because a conversion always happens before a default. Hence, the CDS implied default intensity can be justified as a lower bound of the conversion intensity.

3 This differs from the equity derivative approach in which the conversion time is proxied by the first passage time of the stock price to an implied threshold, in which the stock price volatility affects directly the CoCo bond price through the conversion probability.