Empirical Study On The Pricing Of Convertible Bond In Mixed Sub-fractional Jump Diffusion Environment

Since the promulgation of new regulations on refinancing in 2017,the market scale of convertible bonds has witnessed rapid expansion.In 2019,the newly raised funds of convertible bonds reached 268.8 billion yuan,which has exceeded the total amount of IPOS in that year and has become the most popular financing method for companies.Since convertible bonds have various flexible and complex terms,while gaining the advantages of derivatives,they are also accompanied by certain risks,so all participants need to fully understand the operation mechanism of convertible bonds,and reasonable pricing is an important part of it.A perfect pricing model is conducive to the benign development of the convertible bond market.According to the domestic and foreign scholars to the actual financial market research,found that financial asset price changes with auto correlation,the characteristics of non-stationary increment and jumping,this paper decided to adopt a sub-fractional Brownian motion environment with a jump to pricing convertible bonds,the overall pricing method according to the Shanghai stock exchange in the definition of convertible bonds,namely the convertible bonds is decomposed into bonds and options the sum of two parts.The bond part of convertible bonds adopts the sum of discounted cash flows of each period,among which the calculation of discount rate adopts the risk compensation method in financial management accounting.Convertible bond options section is calculated using the partial differential equation,the method is deduced by means of the theory of the Delta hedge time score jump diffusion process and mixing time score under the jump diffusion process of partial differential equations and boundary value conditions,and then using variable substitution method,transfer equation for the cauchy problem of heat conduction equations,and then obtains the solution of equation,This paper also innovatively considers the option value,and then combines these three parts of the price to get the price of convertible bonds in the mixed fractional jump diffusion environment.The implementation of the strategy of "double carbon" according to the country,need to speed up the construction of new power system,electric power enterprises to develop the new energy power,this will force the industry to refinance scale increase.Therefore,in the empirical analysis part,in order to reflect the practical value of the model,this paper analyzes eight large-scale convertible bonds in the domestic power industry to verify that the model in this paper can indeed provide theoretical support for the smooth issuance of convertible bonds in this industry.Due to the large number of parameters in the model in this paper,in order to ensure more accurate estimation of each parameter,Python software is adopted to further use genetic algorithm for fitting within the estimation range obtained from given historical data.Later,on four different credit risk of convertible bonds for more than a year of track test,the results show that the start first half of the fitting effect is significantly less than half a year later,and mixing time score jump diffusion model is superior to the traditional BS model generally,so this paper think that mixing time score jump diffusion model is effective,for convertible bonds provide participants a better theoretical basis.