Binomial Tree Model for Convertible Bond Pricing within Equity to Credit Risk Framework

TL;DR

This paper introduces a binomial tree model for convertible bond valuation that accounts for credit risk within the equity-to-credit risk framework, demonstrating convergence to a continuous-time model and analyzing key parameters.

Contribution

It develops a novel binomial tree approach for convertible bond pricing under credit risk, bridging discrete and continuous models within the equity to credit risk framework.

Findings

Model converges to Ayache et al.'s continuous-time model

Analyzes transition probabilities and threshold effects

Provides an alternative to existing price dynamics models

Abstract

In the present paper we fill an essential gap in the Convertible Bonds pricing world by deriving a Binary Tree based model for valuation subject to credit risk. This model belongs to the framework known as Equity to Credit Risk. We show that this model converges in continuous time to the model developed by Ayache, Forsyth and Vetzal [2003]. To this end, both forms of credit risk modeling, the so-called reduced (constant intensity of default model for the underlying) and the so-called synthesis (variable intensity of default model for the underlying) are considered. We highlight and quantify certain issues that arise, as transition probability analysis and threshold values of model inputs (tree step, underlying stock price, etc.). This study may be considered as an alternative way to develop the price dynamics model of Ayache et al. [2003] for convertible bonds in credit risk environment.