The Research Of Chinese Convertible Bonds Pricing Based On The Term Structure Model Of Interest Rate

Convertible bonds which have become an important type of financing instrument appear in China security market for few years,but the pricing of which is complicated. It is of great significance to evaluate convertible bonds for issuing companies designing issuance provisions, investors reasoningly investing, and convertible bonds market developing healthily. This paper studies the valuation of convertible bonds based on the theories of modern financial mathematics and financial engineering, making use of finite difference method and finite element method.Three topics is researched in this paper:firstly, this paper attempts to broaden the limitation of invariable interest rate which is latent in the hypothesis of Black-Scholes option pricing model according with the reality of China convertible market; Secondly,because the participants of China convertible market like to use the easily-operated Black-Scholes option pricing model to price convertible bond,this paper studies the accuracy of this model and the difference between numerical solution and analytic solution;Finally,this paper studies the biases between the theoretical prices and market prices and whether the market prices is underestimation and why.Therefore,firstly the fault-free term structure of interest rate(TSIR) is induced by the Polynomial Spline function model for the samples of 62 treasury bonds from Shanghai Stock Exchange and Shenzhen Stock Exchange,and its efficiency for pricing treasury bonds is verified.Then,as the interest rate for pricing convertible bonds in China is constant,and namely has no considering the change of TSIR,a new method of pricing convertible bonds by combing the fault-free term structure with Black-Scholes option pricing model,finite difference method or finite element method is proposed.and this new method is used in the empirical research by the pricing of 11 qualified convertible bonds samples on January 4th,2007.The result indicates that the TSIR model is relatively efficient for the pricing convertible bonds and the the accuracies of pricing have obviously improved.In addition,the market price is underestimated and appropriate explanation is given.Secondly, the solutions of convertible bonds by the numerical simulating technique (finite difference method and finite element method) and Black-Scholes option pricing model are calculated and compared in this paper.we find that the numerical solutions have little inaccuracy than the analytic solution,but the differences between the finite difference method and the finite element method is very small which can be nearly ignored.Finally,the influences of interest rate and coupon are studied one by one which have close relationship with the pricing method.