Research On Convertible Bond Pricing Based On B-S And LSM Model

Throughout the world,the history of convertible bonds has been more than 170 years,and has been developed in China for 26 years.Because it combines stock,bond and option,convertible bonds play a role in promoting capital market development and direct financing of enterprises,and become a very important part of the financial market.However,the characteristics of various options bring difficulty in pricing.The purpose of this paper is to study the pricing model of convertible bonds.This paper introduces the GARCH volatility and compares the accuracy of BS formula(Black-Scholes formula)with the LSM model(Least squares Monte Carlo simulation)and this paper improved the BS formula,added redemption and resale clausing to the BS model to explore a convertible bond pricing model suitable for China.This paper first expounds the research background and significance of convertible bonds.Then,this paper summarizes the existing convertible bond pricing literatures at home and abroad,and draws the following conclusions:The research methods mainly include BS pricing formula,binary tree method,finite difference method and Monte Carlo simulations,and summarize the least square Monte Carlo simulation method that can solve the characteristics of American options for convertible bonds and solve the path dependence characteristics.However,since the domestic convertible bonds will adjust the conversion price(generally downward adjustment)in the case of corresponding dividend distribution,this also applies the pricing method of European options for convertible bonds with American option methods(mainly The BS formula)laid the theoretical foundation.Therefore,this paper uses the B-S formula and the LSM model to price the Everbright Convertible Bonds and the Guomao Convertible Bonds.Next,the paper explains the characteristics of stocks,debts,and options of convertible corporate bonds.In addition to the coupon price,maturity time and coupon rate of the bonds,the convertible bonds also contain complex provisions,such as the rights to convert shares,redeem,and lower the price of the shares,which have greatly improved the difficulty of the pricing of corporate bonds,we can’t just consider convertible bonds as ordinary bonds with a single bullish American option to calculate its theoretical price,but should take into account its passive conversion and active resale.At the same time,this paper also sorts out the past development history and market scale of China’s convertible bonds,and draws the practical significance of convertible bond pricing research in market development and investment and financing.In this paper,the BS formula and the LSM model are used to price the convertible bonds in the sample.The study finds that the BS formula has higher error rate than the LSM model regardless of whether the redemption and resale clauses are considered,but the improved BS model considering the redemption and resale clauses can significantly improve accuracy.First of all,this paper calculates the absolute value about the Everbright Convertible Bonds and the Guomao Convertible Bonds of the difference between the theoretical price and the actual price on the day divided by the actual price,that is the error rate.It is found that the pricing accuracy of the LSM model is higher,and then the two opening price daily since the listing of the convertible bonds were priced and the same conclusion was found.This paper also calculates the daily price of 110 convertible bonds in the market in 2018.The three models are used to derive the theoretical opening price of each day.The t-test shows that the LSM model error rate is significantly smaller than the BS formula and the improved BS model.The conclusion that the LSM model is more accurate is also obtained.