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Mathematical Problems in Engineering
Volume 2014, Article ID 381943, 13 pages
http://dx.doi.org/10.1155/2014/381943
Research Article

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

School of Business Administration, South China University of Technology, Guangzhou 510640, China

Received 26 December 2013; Accepted 9 April 2014; Published 19 May 2014

Academic Editor: Fenghua Wen

Copyright © 2014 Wei-Guo Zhang and Ping-Kang Liao. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.