Research On Option Pricing Based On GARCH-SVM Volatility Modeling For Improved B-S Model

As one of the core theories in financial mathematics,option pricing has always been favored by scholars at home and abroad.Since the establishment of Black-Scholes option pricing model,option pricing theory has developed rapidly.There are parametric models mainly based on the improved Black-Scholes option pric-ing model and also non-parametric models such as machine learning and neural network methods with the development of computers.The advantages of the two types of models are different.The thesis grasps the respective advantages of the two types of models,and cleverly combines the non-parametric model and the parametric model,and us-es the advantages of the SVM non-parametric model to improve the GARCH volatility parameter model.It can not only take advantage of the processing advantages of the SVM model on limited samples and non-linear data,but also retain the fitting of the real financial market volatility aggregation,the logarith-mic return peak and thick tail distribution,and the heteroscedasticity fitting of the underlying asset return rate on GARCH model.It has the characteristics of both financial time series models and machine learning methods.At the same time,kurtosis and skewness are introduced,the classic B-S option pricing model is improved,and the GARCH-SVM option pricing volatility model based on the improved BS model is innovatively established,and it is applied to the Shanghai 50ETF options in the China Shanghai Stock Exchange market for the first time.The main work and innovations of this thesis are as follows:1.Research on Option Pricing Based on GARCH ModelThe thesis firstly derives the generalized autoregressive conditional heteroscedas-ticity(GARCH)model from the stationary financial time series model.Secondly,it collects and preprocesses the sample data of the Shanghai 50ETF options from November 1,2019 to November 18,2020;then,it analyzes the effectiveness of the sample data in terms of stationarity,autocorrelation and partial correlation,and ARCH effect so as to establishes a GARCH time-varying volatility predic-tion model for the pricing of Shanghai 50ETF options.Finally,the GARCH time-varying volatility prediction model is used to introduce the time-varying volatility sequences of the Shanghai 50ETF options,which are used as the input variable of the B-S model and the improved B-S model,so the option pricing prediction of the GARCH model is realized.2.Research on Option Pricing Based on SVM ModelThe thesis innovatively introduces the support vector machine model into the Shanghai 50ETF options in the China Shanghai Stock Exchange market.Firstly,it derives the ?-insensitive support vector machine regression model in detail.Secondly,it selects(S/K,K,?,t,r)as the input variable of the SVR model,and the option daily closing price y as the input variable.Then,the Shanghai 50ETF option input and output sample data is divided into training set and test set,and the original data is normalized and preprocessed.Next,grid search between[-10,10]x[-10,10]and 8-fold cross-validation are used to determine the value of the optimal parameter combination(?,C,c).The training set is used to train the model which is selected by the SMO algorithm.Finally,the test set data is used in the SVM option pricing model determined in the model selection,and the obtained predicted value is denormalized to realize the prediction of the SVM model on the Shanghai 50ETF option.3.Research on GARCH-SVM Option Pricing Volatility Model Based on Im-proved B-S ModelThe thesis flexibly introduces kurtosis and skewness,and establishes an im-proved BS model.Meanwhile,it innovatively improves the parameter estimation method of the GAECH parameter model by replacing the maximum likelihood estimation(MLE)with the SVM non-parametric model,so it innovatively pro-poses The GARCH-SVM option pricing volatility model based on the improved BS model,which is applied to the China Shanghai 50ETF options market for the first time.4.Error Analysis and Model ComparisonThe thesis selects four evaluation indicators of RMSE,MAE,MSE and MAPE,and compares and analyzes the prediction error and prediction effect of the B-S model,the improved B-S model,the GARCH-B-S model,the GARCH-improved B-S model,the SVM model,the GARCH-SVM-B-S model and the GARCH-SVM-B-S model.In summary,the prediction effect of the B-S model improved by skewness and kurtosis is significantly better than the traditional B-S option pricing model;the option pricing power of the B-S model whoes input variable uses time-varying volatility estimated by GARCH volatility modeling rather than the constant volatility has been improved to a certain extent;SVM non-parametric model is significantly better than the traditional parametric model in option pricing effect(B-S model and GARCH model);the machine learning of SVM method for the parameter estimation of the GARCH volatility model is significantly bet-ter than the traditional maximum likelihood method(MLE);the GARCH-SVM option pricing volatility model based on the improved B-S model has the best performance in the prediction of the Shanghai 50ETF option price among the seven models.