| The Black Scholes Option Pricing Model has laid the foundation for the rational pricing of financial derivative instruments such as stocks,bonds,cur-rencies,and commodities.Because of the self-similar characteristics of the financial market,its development model,the fractional Black-Scholes mod-el driven by fractional Brownian motion,has received extensive attention in recent years.In practical applications,model parameter estimation is the pri-mary issue.Therefore,the parameter estimation for the Hurst exponent H,the volatility coefficient σ2,and the drift factor μ,needs to be systematically studied in the fractional Black-Scholes model.In this paper,we assume that all three parameters are unknown and the data is obtained from discrete obser-vations.In the paper,we propose three methods,RVL method,RLL method,and CMLE method,to simultaneously estimate three unknown parameters.This paper gives the estimation theory,simulation,empirical analysis,and application of the parameter estimation in the option pricing.Therefore,the theory can be directly applied to option pricing,portfolio allocation or risk management in the financial field,which has a high guiding significance for actual financial applications and management.Through research we found that the RVL model is more general than the RLL model and CMLE model for two reasons.First,under the condition that the Hurst parameter is unknown in RLL,the stability of σ2 and μ is greatly damaged,so that RLL can only be applied to the condition when the param-eter H is known.While for the RVL,the stability of the three parameters is within an acceptable range.Secondly,in processing large data samples,the CMLE model requires longer computation computation time while the improved accuracy is limited.Therefore,the CMLE is more suitable for situ-ations where the sample and the accuracy should be high.Therefore,in the empirical analysis of the Shangzheng 50 ETF,RVL has a better performance.In the empirical study,we apply the parameters estimated by RVL to the pricing models of three European call options,and find that compared to the traditional Black-Scholes(BS)option pricing model,the price calculated by the fractional Black-Scholes(fBS)model match market prices better.This paper is divided into seven chapters.The first chapter introduces the research background for the project and its literature review.The second chapter describes the preliminary knowledge of Brownian motion,fractional Brownian motion,Black-Scholes model and fractional Black-Scholes model.In the third chapter,three methods used to estimate the three parameters H,σ2,μ in the fractional Black-Scholes model involve the incomplete maximum like-lihood estimation and complete maximum likelihood estimation.The fourth chapter introduces the application of parameter estimation in option pricing.It mainly explains the rationality of adopting Ito type Black-Scholes model.In the five chapter,the numerical simulation analysis of the above-mentioned estimation method is carried out.In the sixth chapter,the parameter estima-tion method is applied to Chinese 50 ETF options.Chapter seven summarizes the full paper. |
