The Pricing Of Convertible Bond With Dynamic Credit Risk

Convertible bond is a new financing tool that can be financing for Enterprise and helpState-stock favoringly withdraw from the market. Because convertible bond is a hybrid natureof containing elements of both debt and equity, it gets extensive attention of investors andcompanies all around the world since it's issued, and is also getting attentions of market. Inoverseas, Convertible Bonds have become essential constituent of every county's capital market.In our country, Convertible bond is introduced to our country's capital market in 1990's. Sincethat time on the market of the Convertible bond had made a great progress . Convertible bondbecomes wider foreground in the field of financing for Enterprise and the State-stock withdrawingfrom the market with the reform of market economy system becoming deep and perfect.The issue of the Convertible bond will drive the capital market to be comprehensive devel-opment, and especially make private hi-tec enterprises in the process of growing up and financialdesign of state-owned stocks withdraw have a better foreground. It is to say that Convertiblebond market will have immense potential in our country. Therefore, studying the pricing of con-vertible bond and discussing the value of convertible bond will have a lot of meaning guidanceif we look forward Convertible bond practice.The further discussion of convertible bond value in this thesis is on the basis of predeces-sors'research. Convertible bonds are much more di?cult to value than the stocks and straightbonds because of their complex structure which include convertible options, callable clauses andput-able clauses and so on. Besides, the convertible bonds value is in?uenced by the creditrisk of Enterprise and the dilutedness of stocks when the convertible bonds owners convert thebonds into the stocks. However, the last two factors were not enough regarded even ignored inthe research on the convertible bonds in the past. Therefore, this thesis considers the value ofconvertible bonds in?uenced thoroughly by the callable clauses, put-able clauses, credit risk anddilutendness of stocks on the basis of predecessors who had research the convertible bonds onlywith callable clauses and put-able clauses.The reason is that the Chinese listed companies exist the reality of ownership Separability of currency stocks and non-currency stocks, and the credit risk exist in the companies strikingly?uctuate up and down, in the process of pricing the convertible bonds in this thesis, the firstwe make the credit risk of Enterprise to be dynamic, then add the dynamic risk to the free riskinterest as a discounted factor. Besides, we consider the reality that dilutedness of stocks thatin?uence the convertible bonds value when the convertible bonds owners convert the bonds intothe stocks at the time expiry date, in fact, this reality can not be ignored. At last , we give outthe formula of pricing the convertible bond value with the martingale way and take the NanJing Shui Yun company's convertible bonds as a example to check the model.The article includes five parts:The first chapter is preface, in this part mainly introduces the background of convertiblebonds and research content in this thesis.The second chapter mainly introduces the summary of convertible bonds, which containthe meaning of convertible bonds, the characteristic of convertible bonds, and some parametersand clauses in?uencing the value of the convertible bonds, these parameters and clauses includethe first conversion stock price, convertible bonds expiry date, volatility, free-risk rate, marketrisk, credit risk, convertible bonds interest,callable price,put-able price, callable clauses put-ableclauses.The third chapter mainly introduces some preparation of knowledge, which is ready for thepricing of convertible bonds in the fourth and fifth chapter. The content contain Ito¨process,Ito¨formula,Girsannov theorem and so on.The fourth chapter gives out the formula of credit risk and make it to be dynamic underthe fact of Chinese companies by using the result of KMV model:Where t is current time, T is expiry time, F is face value, Dt is the bond value of time t, ris risk-free interest rate. By using the option pricing way we can get Dt. Then taking the NanJing Shui Yun company as a example to figure out its credit risk at di?erent time between 10thNovember 2006 and 19th July 2007.The fifth chapter gives out the formula of pricing convertible bonds with the martingaleway after analyzing the in?uenced parameters and clauses of convertible bonds: Where Vt1 is value of convertible bonds considering callable clauses, credit risk and thedilutendness of stocks, Vt2 is value of convertible bonds considering put-able clauses, credit riskand the dilutendness of stocks. Here, taking simple average for the value seems not reasonableaccording to the theory, but from the result of the practice analyse, we can see the theory valueto dovetail with the real value very much, there is only 0.0520% average error in the samples, sowe can say that this hypothesis is reasonable, we also say that the advantage from the callableclauses for the issue companies and that from put-able clauses for the bonds owner is balanced.In a word, the convertible bonds value formula giving by the martingale way thoroughlyconsidering the callable clauses, put-able clauses, credit risk and dilutendness of stock is quiteaccurate. This will help the convertible bonds issue companies, investors, supervisory institu-tions and agency institutions to realize the mechanism of pricing convertible bonds, finally amature and sane risk-avoid financing tool will set up in our country in result which will drivethe bond market to be development.