Pricing Contingent Convertible Bonds with Capital-Ratio Trigger and Default Risk

Abstract

Contingent convertible bonds (CoCos) are hybrid instruments which are characterized by both features, debt and equity. CoCos are automatically converted into equities or written down when the capital-ratio of the issuing bank falls below a contractual threshold. The capital-ratio has been used as a measure for judging bank's nancial health. After Basel III, regulatory authorities start to apply more strict capital requirement of banks to reduce the chance of use of taxpayers' money in the distressed situation. This paper studies the pricing methodology for CoCos with a capital-ratio trigger and issuing bank's default risk. We derive a semi-analytic formula for a theoretical value of CoCos being reflected both risks: conversion risk and default risk We assume that the equity price follows a geometric Brownian motion and the debt level is an unknown value which is revealed only at time of conversion but its distribution may be progressively estimated with market information. Furthermore, we dene rm's default as the moment that a capital-ratio hits a hypothetical threshold which is less than the trigger level. We quantify banks' default risk by using a barrier option pricing approach. Finally, we compare theoretical results with those from Monte Carlo methods and analyze the price sensitivity of CoCos for risk management. Numerical tests show the efficiency and accuracy of our formula.