Pricing Chinese Convertible Bonds with Dynamic Credit Risk

School of Economics and Management, Beihang University, Beijing 100191, China

Received 14 March 2014; Accepted 23 May 2014; Published 9 June 2014

Academic Editor: Chuangxia Huang

Abstract

To price convertible bonds more precisely, least squares Monte Carlo (LSM) method is used in this paper for its advantage in handling the dependence of derivatives on the path, and dynamic credit risk is used to replace the fixed one to make the value of convertible bonds reflect the real credit risk. In the empirical study, we price convertible bonds based on static credit risk and dynamic credit risk, respectively. Empirical results indicate that the ICBC convertible bond has been overpriced, resulting from the underestimation of credit risk. In addition, when there is an issue of dividend, the conversion price will change in China’s convertible bonds, while it does not change in the international convertible bonds. So we also empirically study the difference between the convertible bond’s prices by assuming whether the conversion price changes or not.

1. Introduction

Convertible bond is an innovative and complex financial instrument which can be converted to the issuer’s stock at some specified circumstance. It is hard to be valued because of its characters of both equity and bond, in addition to its varieties of terms. China’s convertible bond market is an emerging market, so it is important to value the product considering some changes compared with the existed valuation methods.

Theoretical research on convertible bonds was initiated by Ingersoll [1 ], who applied the Black-Sholes-Merton model of pricing options. Following his work, Brennan and Schwartz [2 ] firstly used corporate value as the basic variable to price convertible bonds. However, corporate value was soon replaced by stock price for its simplicity of observation and measurement, which was first introduced by McConnell and Schwartz [3 ]. Brennan and Schwartz [4 ] considered stochastic interest rate firstly and constructed a two-factor pricing model for convertible bonds. Then, stochastic credit risk was introduced by Davis and Lischka [5 ]. From the above tendency we can see that researchers gradually added factors to increase the accuracy of valuation. To solve the more and more complex models, Monte Carlo simulation became widely used. Longstaff and Schwartz [6 ] firstly introduced the least squares Monte Carlo (LSM) to price American options. Following them, Moreno and Navas [7 ] studied the robustness of LSM method for pricing American options; Stentoft [8 ] studied the convergence of the LSM approach. Due to its significant advantage in pricing derivatives, LSM method was soon applied to the valuation of convertible bonds, such as the work of Crépey and Rahal [9 ] and Ammann et al. [10 ].

Credit risk is an important factor in convertible bonds valuation and is paid more attention than before in China. Currently, there are two methods to measure the credit risk. The first one is credit spread, which is firstly used by McConnell and Schwartz [3 ] to value convertible bonds.Following their work, Tsiveriotis and Fernandes [11 ] split convertible bond into two components: a cash-only part, which was discounted by risky interest rate, and an equity part, which was discounted by risk-free interest rate. The second method is to use default density, which was used by Duffie and Singleton [12 ] to price corporate bonds. Then, Ayache et al. [13 ] applied default density to convertible bonds, deriving a partial differential equation for valuation. Comparing the two methods, the first one is more widely used for its simplicity and convenience. However,the estimation of the spread is essential.

To get more accurate price, researchers began to employ dynamic credit risk. Davis and Lischka [5 ] supposed that hazard rate obeys a Brownian motion, with the Vasicek model of interest rate, and then established a two and a half model. But they did not verify the effect of the model using real data.

Currently, there is not any model applying dynamic credit risk to price convertible bonds. In addition, when there is a distribution of dividend, the conversion price will change in China’s market, while it does not change in the international market. In this paper we will study the pricing of China’s convertible bonds using dynamic credit risk and then empirically study the difference between the prices obtained by assuming whether the conversion price changes or not.

The rest of this paper is organized as follows. Section 2 gives the basic framework of convertible bond pricing by least squares Monte Carlo simulation. Section 3 derives the equation of dynamic credit spread. Section 4 is the empirical part, including the effect of dynamic credit spread and the comparison of price obtained by assuming whether the conversion price changes or not. Finally, Section 5 concludes the paper.

2. Basic Framework of Convertible Bond Pricing by LSM

Besides the common debt, convertible bonds are embedded with many options, such as conversion option, call option, put option, and option to lower the conversion price. So, we should compare the value of these options comprehensively when pricing the convertible bonds. At the expiration, the final boundary can be