Pricing Convertible Bonds With Default Risk And Empirical Research

This thesis studies the pricing theory of a class of credit derivative securities with default risk and does empirical researches on some convertible bonds of our securities market.First, we set some models that can meet the requirements of stock prices and the market interest rates, and we make some reasonable assumptions of the company's default risk. On the basis of this, we set up a partial differential equation using no-arbitrage theory for pricing convertible bonds. Then, combining with the call provisions, conversion provisions and the default risk assumptions of the convertible bonds, we convert the equation to a linear complementary problem.In consequence of the fact that the value of convertible bonds is strong path dependent on the stock price process and that the terms of convertible bonds are very complex, so we can not find out its analytical solution and we can only solve the problem using numerical algorithm. Therefore, we solve the problem using operator splitting and fixed point iterative method based on finite difference method and analyze the stability, convergence, existence and uniqueness of the solution. In this way, we get the feasible numerical method of the convertible bonds pricing theory.At last, we do empirical researches on some convertible bonds of our securities market. The comparative analysis of the convertible bonds value with the stock price and market interest rates shows that the convertible bonds value is highly positively related with the stock price but is negatively related with the market interest rates. Furthermore the comparative analysis of the actual price with the theoretical price indicates that our model is suitable for our market and can better simulate the changing trend of the convertible bonds price. Based on the results of our empirical research, we find that the convertible bonds are undervalued in normal circumstances. When the convertible bonds in the in-the-value conditions, the underestimate degree is low, otherwise, the underestimate degree is high. By analysis, we think our convertible bonds market is not perfect enough and our suggestion is that we should promote its development by reducing the issuance restrictions, perfecting information, reforming the institutions, simplifying the terms and expanding the issuance size of convertible bonds.