Study On The Pricing Theories And Numerical Calculation Methods Of Convertible Bonds

Convertible bonds are financial derivatives which develop fast. The correct valuation of convertible bonds is conductive to the healthy development of the market. In this thesis, this thesis enucleates two models for the pricing of the convertible bonds based on the terms of the convertible bonds at first. One is the two-factor pricing model based on stock price and rate, the other is the pricing model based on martingale method. Then I put forward the binomial tree numerical method and Monte Carlo simulating numerical method based on particial least square method(PLS). In the binomial tree model, I identify the put and call conditions by judging the simulated stock price situations of each node. And I give the algorithm for components extracting based on PLS. To study the influence of the interest rate, I introduce the CIR model into the Monte Carlo simulating model of the pricing. Then I give the algorithm of convertible bond pricing based on PLS Monte Carlo simulation.In this thesis, I do empirical study of pricing on Chengxing convertible bond. Using the EVIEWS and MATLAB sofrwares, this thesis adopts GARCH model and Generalized Method of Moments(GMM) to estimate the volatility of the logarithmic rate yields of the underlying stock prices and the stochastic interest rate respectively. Then this thesis do pricing research on Chengxing convertible bond by programming on MATLAB. The empirical results show that the trend of the theoretical prices of all the numerical methods presented above are consistent with the market prices in the pricing period. When the degree of moneyness is relatively higher, the deviations of the theoratical price and market prices are relatively higher because of the blind emotion of the market. This research result can guide the investors to invest rationally. Besides, the empirical results show that there is bubblethe in the market prices of the Chengxing convertible bond. I think that the differences of the pricing are related to the choosing of the models, the recession of the convertible bond trading, the lack of the short mechanism and so on.