The Empirical Research About Chinese Listed Convertible Bonds Pricing Based On An Amended Trinomial Tree Model

The convertible bond is a special security of the company issued legally by theissuer, which can be converted into a certain number of underlying securities by acertain percentage or price within a certain period. The convertible bond has excellentfinancing and investment functions, which make it to be one of the fastest growingfinancial derivatives currently. Over the past10years, some domestic scholars didresearch about the convertible bond pricing only by combing foreign models withChinese actual data and often ignored assumptions and parameters of foreign models,which were not suitable for China, the result was the efficient of pricing was not high.The pricing model which is suitable for Chinese convertible bonds market has notbeen designed and therefore developing the pricing model which is suitable forChinese convertible bonds market based on Chinese actual has an importanttheoretical and practical significance. Overall, aspects which mainly impact theaccuracy of convertible bond pricing are: The selection or development of pricingmodels; the estimation of model parameters; the mathematical expression of the valueof the terms embedded in convertible bonds. The paper did research about above threeaspects:(1) Based on Chinese convertible bonds market and the pricing efficiency ofthe existing models, choose the traditional trinomial tree model and for the defects ofthe trinomial tree model,derive the relationship of movement rule of the underlyingstock price in Chinese convertible bonds market, which is the basis for derivation ofthe amendment trigeminal tree model;(2)Derive the calculation formula of theimportant model parameters: the volatility of the underlying stock in China;(3)Derivethe mathematical expression of the value of the terms embedded in convertible bonds.Above aspects are also three innovative points of this paper and the empirical resultsobtained are also different with previous conclusions and they are also the maindirection to improve the efficiency of pricing models for convertible bonds in thispaper. Use the above three conclusions and the actual data of19listed convertiblebonds in Chinese convertible bonds market currently and the MATLAB software, wecan get the pricing efficiency of the traditional trigeminal tree model and the amendedtrigeminal tree model. Empirical results show that both the traditional trigeminal treemodel and the amended trigeminal tree model have high pricing efficiency, but theamended has higher pricing efficiency.The specific content of the article is as follows：Clarify the research backgroundand significance; summary the literature; introduce the organizational structure and research ideas of this paper.Overview the knowledge of the convertible bonds,including the definition and elements of convertible bonds; the development historyand current status of convertible bonds; introduce common terms of convertible bonds;analysis pricing characteristics of convertible bonds; Finally, a brief introduction ofthe development situation about convertible bonds in China. Introduce and deducetraditional pricing models and methods of convertible bonds and then compare to theirrespective advantages and disadvantages. Analyze and deduce the traditional pricingmodel which has higher pricing efficiency than the other traditional models andanalyze its related pricing factors: with the actual data, deduce the formula of thevolatility of the underlying stock; analyze the embedded terms and get themathematical formula of value of embedded terms. Then apply empirical results toprice the19listed convertible bonds in Chinese convertible bonds market currently,combining with the MATLAB software, we can get the model price. By comparingthe actual price to the model price, we can calculate the pricing difference and thepricing efficiency of the traditional trigeminal tree model. For the question that thetrigeminal traditional tree model subjectively set the motion law of the logarithm priceof the underlying stock, we can use the data of235trading days of Chinese19listedconvertible bonds during2011to deduced the new relationship of the motion law ofthe logarithm price, which is suited to Chinese convertible bonds market. Deduce theamended trigeminal tree model based on the new relationship, and then combine theamended trigeminal tree mode with the actual data of currently19listed convertiblebonds in Chinese convertible bonds market currently and MATLAB software to do anempirical test, we can calculate the pricing difference and the pricing efficiency of theamended trigeminal tree model.Analyze pricing efficiency of the traditionaltrigeminal tree model and the amended trigeminal tree model and get the pricingmodel which is more suited to China’s convertible bonds. Finally, give innovationand by analyzing the results of the empirical research; put forward feasiblesuggestions about the better and faster development of pricing models and theinadequacies of the research.