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Because of its creditor’s rights, equity, and options, convertible bonds have been developed rapidly since its emergence and have become one of the main tools in the financial market. One of the core problems of convertible bonds is pricing. The research on the pricing model of convertible bonds in China is relatively late. Most of them use foreign technologies, but they are quite different from the actual situation in China, and most of the models are characterized by a single factor. Therefore, this paper puts forward the nonarbitrage pricing model in the stock market and the application of the finite element numerical solution in the value of convertible bonds. The biggest innovation of this paper is to design a combined pricing model by using the model of nonarbitrage pricing theory and finite element numerical solution. The model combines the advantages of the nonarbitrage pricing theory and finite element numerical solution, and through the design of this paper, the model effectively improves the calculation accuracy and is suitable for most of the current market environment. While improving the comprehensive performance of the pricing model, it also simplifies the calculation methods and steps. In order to further verify the actual effect of the pricing model in this paper, the traditional binary tree model is taken as the experimental contrast object, including the comparative analysis of the market price and the theoretical price of the convertible bond, the comparative experiment of the prediction effect between the model and the binary tree model, and the analysis of the relative price error of the convertible bond. The results show that the comprehensive performance of the pricing model in this paper is significantly better than the traditional binary tree model. This study has achieved ideal results and can be widely recommended.

Application of Nonarbitrage Pricing Model and Finite Element Numerical Solution in the Value of Convertible Bonds in the Stock Market