Research On Monte Carlo Pricing Method Of Convertible Bonds

This paper studies pricing the convertible bonds of Monte Carlo pricing method. Convertible bond pricing problem is a very complex issue. Attributed to too many variables, the current convertible bond pricing method varied. Convertible bonds are provided with both the nature of the stock and the bonds. Therefore, the traditional pricing models can not be reasonable to calculate the value of the two parts separately. Monte Carlo method prices the bonds by using historical data of underlying stock price and models the path of the bond price, avoiding splitting issue of the nature of the stock and the bonds.Firstly we assume that the underlying stock price follows Geometric Brown Motion. Based on historical stock price volatility we simulate 1000 stock price paths and 1000 SHIBOR paths. We can find three values of convertible bonds in every moment. Conversion value= stock price × conversion ratio. Put value is predetermined in the provision. The holding value changed based on stock prices and SHIBOR, so it can be got through a binary non-linear regression of the stock price and SHIBOR. Compare the three value to get the paths of the bond value. Averaging the bond value in the same moment can predict the bonds price in the future. In order to ensure the accuracy of the forecasts, we must use the appropriate model to describe the movement of the stock price. Besides assuming the motion on the basis of geometric Brown, this paper attempts to use GARCH (1,1) model to describe the stock price movement. The stock price volatility is also very important. This paper uses a GARCH (1,1) model to estimate the future volatility. Comparing the results, the stock price is likely follows Geometric Brown Motion. To demonstrate the applicability of the method, this paper estimates another company’s convertible bonds. Assuming its stock price follows geometric Brown motion, using the GARCH (1,1) model to estimate volatility. The results are very close to the actual price. At last, this paper summarized the advantages and disadvantages of this method. The main advantage is that it is fit for the bonds markets in our country. It does not rely on the company’s equity and debt of internal relations. The main shortcomings of this method is that there are downwardly revised terms in the convertible bonds. This article is based on the constant conversion price. The prediction accuracy of this method is better when the conversion price remain unchanged.