Pricing contingent convertible bonds: A numerical implementation with the hybrid equity-credit model

Abstract

The contingent convertible (CoCo) bond is a loss-absorbing instrument which can be converted mandatorily to common equity when a trigger event happens, such as the bookvalue trigger and the discretionary trigger. The book-value trigger means that once the capital ratio hits the pre-specified threshold, the equity conversion will be activated. The capital ratio is the proportion of capital to risk-weighted assets (RWA), which reflects the financial health of the bank. With the discretionary trigger, the conversion of the CoCo bond will be decided by the regulators according to the financial situation of the issuing bank. In this thesis, we examine the hybrid equity-credit model suggested by Chung and Kwok (2016), which combines the book-value trigger and the discretionary trigger, assuming that the capital ratio has a mean-reversion movement and that the stock price follows a geometric Brownian motion with jumps. Furthermore, we perform a real world implementation of the Credit Suisse CoCo bond by calibrating the parameters of the hybrid model against market data and applying both Monte Carlo simulation and the so-called Fortet algorithm. As an extension, we add a Cox, Ingersoll and Ross (CIR) framework to the equity-credit model to reflect the dynamic of the interest rate. We present the results of the CoCo prices, the calibration errors and the implied conversion probabilities as well as sensitivity analyses and find several interesting numerical results for the Credit Suisse CoCo bond. For example, the data seems to imply that the CoCo will be converted with almost 100% probability within 2 years from April 2014.