Research On The Valuation Of Convertible Bonds Based On Least Square Monte Carlo Method

The convertible bond is a special type of bond,it is a combination of debt and equity financing tool.Currently,China's convertible bond market is still in the stage of development.Finding a suitable method to price convertible bonds can help promote the healthy development of the market.As the transfer option of convertible bonds is similar to an American option and no classical analytic pricing method such as Black Scholes formula for an American option exist,we rely on numerical simulation method to price convertible bonds.Firstly,this paper introduces the basic concepts and research of convertible bonds,and reviews the classic pricing method of convertible bond and analyses their advantages and disadvantages.Secondly,this paper introduces the Least Squares Monte Carlo method(LSM)to price convertible bonds.Meanwhile,special clauses of convertible bonds are considered in this paper,if the simulation path triggers special clauses,it will be adjusted before the calculation.Estimate and actual price of convertible bonds are compared after the calculation.Based on the classical method,this paper improves the original model in three aspects.In terms of underlying stock volatility,we find that stock volatility plays a crucial role in convertible bond pricing through sensitivity analysis.GARCH(1,1)model is used to estimate the stock volatility instead of using historical fluctuation model.In terms of random number generation,Quasi-Monte method is used to generate random number instead of Monte Carlo simulation,which makes the random number more uniform,and the convergence rate is faster.In terms of the underlying asset path generation,Brown bridge method is used instead of the random walk method.The storage space is saved through this method.Finally,the proposed model is evaluated through pricing Lanbiao convertible bonds.The difference between estimate and real value can be reduced by using GARCH(1,1)model;QMC methods can significantly improve the simulation convergence speed,but the accuracy of the estimation cannot improved through increasing the number of simulations after the simulation number reaching certain level;Brownian bridge can replace random walk to save the storage space without effecting the accuracy of estimation.