The Chinese Convertible Bonds Pricing

The convertible bonds' history is about 150 years in international financial markets. The research of convertible bonds has been developing quickly in recent 40 years. China is a burgeoning market for convertible bonds. There are not many researches which combine both deep analysis of the multiple clauses of the Chinese convertible bonds and theoretical pricing models. The main reason for this situation is that the clauses of Chinese convertible bonds are very complex, and some important clauses such as reset clauses are some extent vague.In order to build a theoretically and practically valuable model, this paper first analyzes all the clauses of the Chinese convertible bonds, especially on the reset clauses, back-sell clauses and redemption clauses. Based on this analysis, we build a mathematical model combining with the peculiarities of Chinese convertible bonds. We solve this model by partial differential equations and presents the numerical results together with some suggestions for the development of the Chinese convertible bonds.In the second part of the paper, we consider a special kind of convertible bonds whose converting price may reset at a predetermined time(a Japanese innovation). Kimura and Shinohara analyze a simple model first, we develop this model and present a more precise one under constant interest rate and obtain a closed form solution by martingale theory and transformations of probability measures. As the duration of the convertible bonds are long, it is more reasonable to assume the risk-less interest rate be stochastic, so under the extended Vasicek model, we obtain an analytical solution of the price of this kind of convertible bonds and present the numerical results.