The Application Research Of Monte Carlo Simulation In Pricing Convertible Bonds

Convertible bonds are complex derivatives and typical path-dependent securities with many embedded options. With the continuous development of China’s convertible bonds market, the researches on the reasonable pricing of convertible bonds will provide the basis for the issuing companies and the investors’analyses of the values of convertible bonds. By Using the Monte Carlo simulation of the least-squares regressions put forward by Longstaff and Schwartz (2001) and taking special modification clauses lowering conversion price, conditional call options and conditional pull options into consideration, this thesis has made theoretical analyses and empirical researches on the pricing of convertible bonds.First the pricing theories of convertible bonds will be reviewed and sorted out and then it can be found that when Monte Carlo Simulation is used for Pricing Convertible Bonds, the influence of different normal distribution and conversion methods on the results is seldom taken into consideration. In response to this situation, the two normally distributed variables transformation methods, including the Box-Muller method and the Moro algorithm of inverse transformation, will be introduced in the second chapter of this thesis. Then in the fourth chapter these two methods will be applied to the pricing of convertible bonds and it can be found that the simulation results of the Box-Muller method are more stable when the simulated path is set. At the same time, when the uniform distribution sequence is replaced by Halton sequence and the Moro algorithm of inverse transformation is used for Monte Carlo simulation, it can be found that using Halton sequence for simulation does not have any advantages. After these comparisons, in the fourth chapter, the Box-Muller method will be chosen to sample the standard normal variables of the uniformly distributed random numbers. Meanwhile, the stock volatility method in the third chapter will be revised and the GARCH model will be adopted to estimate the fluctuation ratio of the stock. As a result, it can be found that the relative errors between the simulated prices and the actual prices have been decreased.This thesis has done empirical researches on13convertible bonds traded on the Shanghai Stock Exchange, calculating their simulation prices within16inconsecutive trading days and comparing them with the actual prices on the market. However, the result is inconsistent with that from some scholars’ empirical researches about the convertible bonds of our country; namely, the market prices of the convertible bonds are obviously underestimated. On the contrary, the conclusion reached from this thesis is that the simulation prices of the samples of convertible bonds are on the average less than0.66%of the market prices and there doesn’t exist the phenomenon that the market prices of the convertible bonds are obviously underestimated or overestimated, all of which will be explained from the investors, the stock market and other aspects.