Pricing Convertible Bonds with Credit Risk under Regime Switching and Numerical Solutions

Wei-Guo Zhang,Ping-Kang Liao

doi:10.1155/2014/381943

Wei-Guo Zhang, Ping-Kang Liao

Open Access

https://doi.org/10.1155/2014/381943

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Abstract

This paper discusses the convertible bonds pricing problem with regime switching and credit risk in the convertible bond market. We derive a Black-Scholes-type partial differential equation of convertible bonds and propose a convertible bond pricing model with boundary conditions. We explore the impact of dilution effect and debt leverage on the value of the convertible bond and also give an adjustment method. Furthermore, we present two numerical solutions for the convertible bond pricing model and prove their consistency. Finally, the pricing results by comparing the finite difference method with the trinomial tree show that the strength of the effect of regime switching on the convertible bond depends on the generator matrix or the regime switching strength.

Highlights

We present two numerical solutions for the convertible bond pricing model and prove their consistency
Convertible bond is a kind of the most important financing instruments, so the convertible bond market occupies an important position in the international financial market
American convertible bond market is the largest market in the world, and it has issued more than 400 trillion dollars in total from 1980 to 2011

Summary

Introduction

Convertible bond is a kind of the most important financing instruments, so the convertible bond market occupies an important position in the international financial market. Lee and Yang [12] presented the unexplained portion of the valuation model of convertible bonds based on MCDM Credit risk is another important factor that affects the value of convertible bonds. Different from previous work, they adopt default intensity to measure the credit risk and build a model by deriving the PDE of the convertible bonds. This idea is introduced to trinomial tree and multifactor model, such as the work of Chambers and Liu [18]. This paper will discuss the pricing convertible bonds with credit risk under regime switching, which take the dilution effect and the debt leverage into account.

Theoretical Model of the Convertible Bond Pricing

Dilution Effect and Debt Leverage

Numerical Solutions

Numerical Example and Analysis

Findings

Conclusions