Option Pricing With Random Arrival CGMY Model Based On Saddlepoint Method

The importance of option pricing is self-evident,which has been studied in the field of financial mathematics.Option has the function of risk hedging and risk avoidance,is an important and significant financial derivative,and is an essential tool for market traders in the transaction.Traditional BSM model is of great significance in solving the problem of option pricing,its application is very extensive,but in some conditions the model assumption does not accord with the actual situation of financial markets,the BSM model is the key of the option pricing model,and the option pricing research to 0)? process based on the option pricing model.0)? process has many properties: independent increment,right straight left limit and stationary increment,with jumps and peak,thick tail characteristics,0)? process can be better characterization and description.This article selects the Shang Zheng 50 ETF options to study in the 0)? option pricing model and non-gaussian base under the saddle point method of option pricing problem.This article mainly studied from four aspects: first,the analysis was carried out on the option theory introduction,including the classic BSM model and the 0)? option pricing model and saddlepoint pricing method based on non-gaussian,0)? option pricing model including the VG model,CGMY model,VG-SA model and CGMY-SA model;Secondly,according to the characteristic function of CGMY-SA model,the cumulative generation function is derived,and the saddle point European call option pricing formula based on nonGaussian of CGMY-SA model is derived accordingly.Numerical simulation of each model is carried out by this method,and comparison is made by combining the fast Fourier transform method and the Fourier cosine method.Thirdly,descriptive statistical analysis is carried out on the logarithmic return rate of Shang Zheng 50 ETF,and normality test is carried out.Levenberg Marquardt(nonlinear least squares)algorithm is used to minimize the mean square error,so as to estimate the model parameters,and obtain the parameter estimation results of each model.Fourthly,according to the parameter estimation results,the option price is fitted by combining the above five models under the fast Fourier transform method,Fourier cosine method and saddle point method based on non-Gaussian,and the obtained results are compared with the real market price to analyze the practicability and effect of CGMY-SA model and saddle point pricing method based on non-Gaussian in the Shang Zheng 50 ETF option pricing.And use APE(mean percentage error),AAE(mean absolute error)and other four statistical indicators to do error analysis.The empirical study in this paper is divided into two parts.The first part is numerical simulation.Through the simulation,it can be seen that the saddlepoint method based on nonGaussian has a good accuracy for option pricing,especially in the virtual part.The second part in combination with the Shanghai 50 ETF,march to buy call options selected 80 price data(40 in the money options,40 out-of-the-money options)are studied,the results show that the through error analysis shows that the result of the fitting 0)? option pricing model for don’t obey the normal distribution and rush thick tail phenomenon description is better than the BSM model;According to the pricing results of CGMY-SA model and VG-SA model,there is no volatility clustering in Shang Zheng 50 ETF during the study period,and the performance of CGMY model is better than other models.In terms of implementation methods,saddlepoint method is better than fast Fourier transform method and Fourier cosine method in pricing virtual options,especially non-Gaussian saddlepoint method is slightly better than Gaussian saddlepoint method.