Research On The Overall Pricing Of Convertible Bonds In Uncertain Environment

Convertible bonds are a kind of compound financial products with "dual nature of stock and bond".Since 2017,with the development of capital market,the convertible bond market has begun to expand.As one of the primary market financing tools and one of the secondary market investment tools,convertible bonds have attracted more and more attention from financiers and investors.For investors,convertible bonds have good time and space liquidity,"Advance can be attacked,retreat can be defended".When the stock price rises,it can be converted into company’s stock to obtain profit opportunities,and when the stock price is low,it can’t exercise the conversion right,hold bonds until maturity,and obtain fixed income.Compared with developed countries,China’s convertible bond market has its own characteristics.There is no way to directly extract the results of mature markets in developed countries.It is urgent to explore and construct a convertible bond pricing model suitable for the China’s convertible bond market.ZL and LSM convertible bond pricing models are mainly based on the Black-Scholes model.In the risk-neutral world,the price of the underlying stocks of convertible bonds follows Geometric Brownian motion.Because of the various rational assumptions in the model,the estimated theoretical results will have a certain degree of deviation from the actual price.There are many reasons for this deviation.It may be due to investors’ incomplete understanding of the convertible bond market,immature interest rate liberalization,very complex terms design,irrational choices by investors and so on.However,a more special point is that it assumes that the volatility of assets is fixed,but the volatility in the actual market is not fixed,but variable,and even uncertain.Therefore,this paper aims to consider the use of G-Brownian motion to derive the underlying asset price process under the condition of uncertain volatility,and on this basis,for the first time,the overall pricing method is used to fully consider the path dependence of the special clauses embedded in the convertible bonds,and the pricing of convertible bonds is studied in order to obtain better results.The article is divided into the following sections:The first part of the introduction mainly introduces the development of China’s convertible bond market in detail,the significance of pricing research on convertible bonds,and summarizes the research on convertible bond pricing by domestic and foreign scholars.The second part is a detailed interpretation of the terms and elements contained in convertible bonds,as well as the overall summary of the particularity of China’s convertible bond terms,so as to better understand and deeply analyze convertible bond products.The third part is a summary of the classic convertible bond pricing model.According to the advantages and disadvantages of the model,ZL and LSM models that can solve the path dependence problem of convertible bond terms are selected for overall pricing.And put forward the overall pricing method based on nonlinear expectation:Firstly,the asset price process based on G-Brownian motion is derived,and then the volatility is estimated by(p-mean-max method.For the first time,the random number of G-Brownian motion and its quadratic variation process is generated by equal probability random sampling variance method,so as to simulate the stock price under uncertain environment,improve the core steps of the overall pricing method of convertible bonds,and lay a theoretical foundation for subsequent empirical analysis.The fourth part is the empirical analysis,which mainly focuses on the pharmaceutical manufacturing industry.According to the characteristics of the pharmaceutical manufacturing industry,the overall pricing method based on the ZL model is selected to analyze the time dimension of the first day of listing and the first year of listing of 14 convertible bonds in the pharmaceutical manufacturing industry.In the classical ZL model,the price of the underlying asset is subject to the Geometric Brownian motion,assuming that the volatility of the asset is constant,and the price deviation of the first day of the listed transaction is predicted to be high,with an average error rate of 7.62%.In cases of where the volatility of the asset is uncertain,the GBrownian motion is used to simulate the underlying asset price,and the ZL model is improved for the overall pricing,and the price deviation of the first day of the listed transaction of the convertible bond in the pharmaceutical manufacturing industry is predicted to be significantly reduced,with an average error rate of 3.34%.After comparison,it is found that the pricing accuracy of the improved model is improved.Then,7 convertible bonds were selected from 14 convertible bonds,and the time back test was carried out one year after listing.It was found that the improved model was partially superior to the traditional model,and the improved model did not show a large deviation when the traditional model had a good fitting effect.The effectiveness of the improved model method and effect of G-Brownian motion based on nonlinear expectation is proved.The fifth part is the summary and outlook,analysis of research results and shortcomings,and how to further improve the pricing model.