Martingale Pricing Research On One Kind Of Convertible Bonds

Convertible bonds is a kind of special mixed financial derivative, investors can choose to get the principal and interests back at the end of a contract like they deal with ordinary bonds, or to exchange convertible bonds into issuers'stock. So it's convertible bonds feature to have properties of both credit and options. The credit property guarantees the minimum rate of return, while the optional property provides the chance of better reward. The convertible bonds has become a favor for investors and capital raisers because of its flexibility, security and high return. Together with the diversity of convertible bonds coming along with various clauses, pricing the convertible bonds is now a highlight subfield in the area of financial derivatives'pricing problems.In this paper, martingale method has been selected to study the convertible bond pricing issue, as martingale is a special stochastic process and has evolved into an important leading edge mathematic tool in the study of modern financial mathematic. especially for the pricing problems of financial derivatives such as options. There have already been some achievements when applying the martingale theory to the pricing issue of convertible bonds, while changing the models of underlying assets' prices is an important way to do such research. It's considered that there is not just random fluctuation but also many unexpected influencing factors existing in reality, so in this paper, the model of stock pricing fluctuation with both random and abnormal fluctuations is adopted to describe the behavior of stock price. This model fits the circumstance with abnormal fluctuation caused by previous financial crisis. The parameters in the model are set to be time functions, which makes the model closer to the constantly changing actual market. Besides that, back buy clause and back sell clause are also under consideration to form a more complicated model. Based on the background formed of this new model and assumption of risk neutral, and with the foundation of theories from subjects such as stochastic process, higher probability and stochastic calculus, the initial price formulas of convertible bond with clauses are obtained by using mathematical tools like Ito theorem, measure transformation, etc. The results of this paper extends the application of martingale in the field of financial derivatives pricing, enriches the system structure of this field, and has laid a foundation for further research on pricing convertible bond.