Convertible Bonds Pricing Based On The Extension Of LSM Model

Refinancing in 2017 after new rules and reduce its new rules,convertible bonds become securities issue market to be bestowed favor on newly gradually,gradually expand the scale and quantity,and because investors can take credit purchase,make investors focus on more and more,are on the market of convertible bond fund,the attention of market increasing heat.At present,convertible bonds in the market are generally embedded with a number of relatively complex terms.It is because of the complexity of terms of convertible bonds that a perfect pricing model of convertible bonds can provide a powerful reference for investors’ investment behavior and a valuable demonstration for the listing price of convertible bonds.Firstly,this paper reviews the pricing theories of convertible bonds at home and abroad,and introduces the theoretical development of b-s model,binary tree model and least square monte carlo model respectively.Then it introduces the definition of convertible bond,the development status of convertible bond market in China,the relevant issuing conditions and basic terms of convertible bond.After that,it mainly focuses on the problems existing in the pricing of convertible bonds.The main research content includes the analysis of the main factors affecting the pricing of convertible bonds and mainly analysis the redemption clauses,terms and turn back equity influence on convertible bonds pricing,terms of redemption for the issuer is equal to the call option,put the terms for investors is equal to the put option,and equity to investors is equal to the call option,the terms and conditions will have an effect on pricing.Then,the cons and pros of b-s pricing model,binary tree model,least square monte carlo(LSM)model and extended LSM model in the pricing of convertible bonds are respectively introduced and analyzed.Although the b-s pricing model is simple in calculation,it is not accurate in pricing each option and ignores the connection between each option,because it is applicable to European option pricing and cannot solve the clause that convertible bonds can be converted into shares in advance.Although the binary tree model can solve the problem of early stock conversion,it cannot solve the problem of path dependence,that is,the underlyingstock price must be higher or lower than a certain percentage of the current stock conversion price for a period of time to trigger the cb clause.Although the LSM model is cumbersome and slow in calculation,it can not only solve the problem of implementing the terms of conversion in advance,but also solve the problem of path dependence.However,the extended LSM model is a pricing model incorporating additional terms of China’s convertible bonds,which has good adaptability to the pricing of China’s convertible bonds.Based on the above analysis,this paper considers the most important features of convertible bonds in China: first,China’s convertible bonds can be converted in advance,that is,it has the characteristics of American options;Secondly,China’s convertible bonds are accompanied by complicated redemption and resold terms,and the trigger conditions of these terms are path-dependent.In this paper,an extended LSM model is selected to make an empirical study on convertible bond pricing.In the empirical part,this paper use of matlab software for our country in 2017 and 2019 offerings of 22 larger issuance scale good pricing convertible bonds in its debut effect test,compare the extension of the LSM model error of the actual price and its debut,the conclusion shows that extension of the LSM model good pricing effect,its pricing on average error rate is 5.45%.Then,based on the improvements on the volatility,considering the convertible bonds mark rush thick tail stock yield distribution and financial asset price volatility agglomeration phenomenon,using GARCH(1,1)model can better analyze these phenomena,and measuring the share price volatility,the replace the historical volatility method to estimate the convertible bond volatility of the underlying stocks,further improvement of extension model of LSM.Finally,empirical results show that the average pricing error of the improved model is 2.78%,and the improved extended LSM model improves the pricing effect of convertible bonds.