Based On The Pricing Of Convertible Bonds Jump Diffusion Process

Convertible bonds is one of the particular securities,which can choose to be ordinary stocks in the transition period, or hold it to abtain the principal and interest until the maturity date.For its own characteristics,the owner of the convertible bonds has the rights to convert it to stocks in the transition period.If you choose to,the convertible bonds holder turn to be a stockholder,not a creditor. All of the characteristics make it has the basis guarantee of minimum rate and may receive as many as income for the investors,but for the ones,who raises funds,it not only issue its put options implied,but also raise the funds at a lower risk,so it is a good security for both the inverstors and the raiser. Thus it take many scholars' attention to study it.Now more and more scholars study to how to price it.Scholars both in domestic and international proposed many pricing models:such as Synthetic Model,Two-brach Model,Accurate pricing Model,Structural Model and Simpler formed Model.In actually fact, the Structural Model and Simpler form Model is a special Synthetic Model,which considered the default risk.Two-brach Model need to know the convertible bonds ultimate value which it is not easy to know,so we can hardly to get the convertible bonds price. Boundary conditions of the Accurate pricing Model is not easily to find. Therefore, this text use the Improve Synthesis Model to carry out the pricing of convertible bonds.The Synthesis Model take the convertible bonds consist of common bond and put option,but the Improve Synthesis Model take the convertible bonds consist of the maximal of common bond and convert value,and plus the pricing of the put option.So we need to price the bond and put option,then we can price the convertible bond.We use discount method to price the common bond,to the put option,it has European Form and American Form.Because of the convertible bond in our country has its own specially features,so we choose the European put option to price it.The formula of the European put option has two,one is based on the diffusion process and the other is based on the geometry of brownian motion.Theoretically,The market share price have changed not only suffered by the balance of the need and supply,but suffered by the economic prospects of the company and the new information of the industry.The former influence we can use the geometry of brownian motion to describe it and the latter's influence we use a process called "jump" to depict it.So jump-diffusion model is better to describe the changes of the actual markets price.This article use software SPSS verify the stock price fluctuations are not obey the geometry of the brown.So this subject choose the European put option model,which beyond the jump-diffusion process, the convert value is execution value,to price the convertible bond.Finally, by empirical research,we introduce ordinal clustering methods, using SAS procedures to price the convertible bonds with the underlying asset following jump-diffusion process, we also price the convertible bonds with the underlying asset following geometric Brownian motion, at last we will compared the two results with the market prices and we found that the results of jump-diffusion model is better.