Comparative And Empirical Study On The Pricing Of Convertible Bonds Based On B-S Model And GARCH Model

The convertible bond which is a kind of complex financial derivative was created in the United states in the 18th century.With the dual nature of dept and equity.convertible bonds not only reduce the financing cost of the issuer but also give investors a certain income guarantee.Therefore,convertible bond have gained high attention from the capital market since it emerged.China’s convertible bond market started late and has a short development history.Now it is still in the primary stage of development.In view of the lack of investment products and insufficient financial innovation in China’s capital market,convertible bond is a effective solution.As an intermediate investment and financing tool,the prosperity and development of the convertible bond market system will be very beneficial to the maturity of China’s capital market and the resolution of financial risks.The focus of this paper is to use the B-S model and the GARCH model to calculate and compare the value of convertible bonds.Among them,in the calculation of the option part,in order to make the final result more accurate,this paper analyzes the influence of various clauses on the theoretical value of convertible bonds from the calculation methods of the two models to correct the results of the primary model.Thus,the two results of "pre-correction theoretical value" and "corrected theoretical value"under the two model methods are obtained.The results show that the results of GARCH model are better than the classic B-S model from the horizontal comparison.In the vertical comparison,the overall corrected result is better than before the correction.In the case selection of empirical analysis,in order to make the analysis more representative and comprehensive,this paper selects four convertible bonds according to the bond rating classification of China’s convertible bond market,and conducts pricing research based on BS model and GARCH model respectively..In order to more clearly compare the pricing results of the model with the actual price,this paper also calculates the theoretical results of one year after the issuance of the four convertible bonds,and dynamically tracks the actual market price.The results show that the results obtained by the two models show that at the initial stage of the market,the theoretical value and the actual price are highly deviated,and the fluctuation is more severe.When the convertible bonds are listed for a period of time,the price tends to be stable,and the revised theoretical value and The deviation of the actual price will become smaller.However,for the two convertible bonds with higher bond ratings,the absolute values of the deviations of the results obtained by the two models are lower,and there is a better fitting effect with the actual price;and the two convertible bonds with lower ratings are The deviation between theory and actual price is relatively large.In addition,the GARCH model results are more stable,can better reflect the market reality,showing the higher the rating of the bond,the closer its theoretical value to the actual price.In the part of empirical analysis,considering that the information value contained in the bond rating results may affect the accuracy of the pricing results,this paper selects four convertible bonds according to the bond rating classification of China’s convertible bond market and prices them respectively based on the BS model.In addition,this paper also analyze the terms of the convertible bonds and correct the pricing results by calculating the value based on the attributes of-the terms.In order to make the contrast more clearly between pricing result and the actual price,this paper calculates the theoretical results of the year after the issuance of the four convertible bonds,and compares them with the actual price.The results show that the results based on the B-S model still deviate from the actual ones,and the degree of deviation is different.However,for two convertible bonds with higher bond ratings,the absolute value of the deviation is only about 4%,which proves the validity of the model to a certain extent;and the theory and practice of two convertible bonds with lower ratings The price deviation is relatively large.Besides,the results also show that the higher the rating of the bond,the smaller the degree of deviation.According to the empirical research results,the reasons for the errors still existing in the revised two types of models are analyzed from the aspects of market maturity,investor cognition,convertible bonds and model parameter estimation.Then,a qualitative solution based on the cause of error is given,in order to provide ideas and research directions for the pricing of convertible bonds in China’s capital market,to promote product innovation of convertible bonds and investors’ understanding of the convertible bond market.Thus contributing to the development of China’s financial market.