Pricing And Empirical Analysis Of Convertible Bonds Based On The Finite Element Method

As an interest rate derivative securities with strong path dependence (Conversion, callability, redemption), pricing convertible bonds has a certain degree of difficulty and complexity. The finite element method is a common engineering calculation in numerical methods, and it has a certain advantage in dealing with the problems with path dependence. Therefore, this paper prices and empirically analyzes these derivative securities with the finite element method.This paper starts from the theory of pricing convertible bonds. Suppose the stock price changes follow geometric Brownian motion, stochastic interest rate follows the CIR model. We use no arbitrage pricing theory derive the arbitrage-free pricing model, which based on stock prices and interest rates. This model is two-factor model, then we use the finite element method to solve the model. In the empirical aspect, we do the empirical research in Xiye convertible bonds, Chengxing convertible bonds and xingang convertible bonds. First, we select the data of underlying stocks and Shanghai inter-bank offered rate (Shibor) from January 5th 2009 to January 5th 2010, and we estimate the parameters of the model, then we calculate the theoretical price of this three convertible bonds from January 6th 2010 to July 31st 2010 using the derived no-arbitrage model and finite element numerical method, and analyze the theoretical price and market price. The results show:The difference between theoretical price and market price is small, within 5%, and the finite element method is a practical numerical calculation method for pricing convertible bonds; The theoretical price and the market price have a high relevance, so the two-factor model is a practical model; The market price is less than the theoretical price, that is to say, the value of convertible bonds is underestimated. Finally, we analyze the causes of differences between the theoretical price and the market price, and we put forward some reasonable proposals for the development of convertible bonds market.