| An option is a derivative product with a special profit and loss structure,options play an extremely important role in the financial market.Option pricing are the basis for the trading activities and risk management.Traditional parametric option pricing models are mostly based on strict assumptions,which are not consistent with the actual situation.Most of these models are too difficult to obtain an analytical solution directly,and have to resort to the means of numerical methods.Besides,the traditional parametric option pricing models are mostly based on fundamental market indicators including strike price and maturity,but cannot consider additional factors such as historical trading variables and media news variables.Machine learning based non-parametric methods provide new ideas for option pricing.Compared with traditional parametric methods,non-parametric methods are fully data-driven,and free of any strict preliminary assumptions.Moreover,the non-parametric methods can provide dynamic relationships between input characteristics and output targets.Unlike stock markets,for those options with similar maturity,there are several options traded at the same time,and these options have comovements.However,the traditional parametric models and the non-parametric pricing model mainly based on machine learning ignore the comovements between options.In this regard,this paper constructs an option pricing model based on convolutional neural network（CNN）.CNN is free of any preliminary assumptions,and can provide the dynamic evolution of the options market.Furthermore,when used to price options,the feature extraction and pattern recognition mechanism of CNN can be used to take the option comovements into consideration.As this kind of comovements exist among options,this paper uses the feature rearrangement mechanism to reconstruct the input option feature matrix,and proposes the FR-CNN model for pricing European options.In addition,parametric and non-parametric models have their own advantages and disadvantages and cannot be generalized.Non-parametric models often require large amounts of data to be trained to establish a functional mapping between inputs and outputs.The traditional parametric methods including JD and SV are based on strict economic theory,and can provide the rules and characteristics of option contracts.They are more stable than non-parametric models.This study proposes an option pricing ensemble learning algorithm based on stacking and boosting ensembling.The ensembling based on stacking uses statistical methods（simple mean method and least square error method）or machine learning（MLP and CNN）.The method integrates the pricing results of all parametric and non-parametric models using a meta learner.The integrated algorithm based on boosting uses the estimation results of a single model,and improves the pricing results by fitting and modifying the residuals.By integrating both parametric and non-parametric models,the pricing performance of a single parametric or non-parametric model is further improved.The unique contributions of this article can be summarized as follows:（1）For the first time,this article uses the Internet media news factor as the influencing factor of option prices to conduct related pricing research.Internet media news affects the fluctuation and volatility of option prices by affecting the trading behavior of investors.However,most existing studies on option pricing have only considered the market variables of options including exercise price,expiration period,etc.It ignores historical trading variables and media news factors.In this regard,this paper systematically describes the three variables including market variables,transaction variables,and news variables that affect or determines the option prices.By constructing different characteristic input combinations,this paper tests various input characteristic combinations under non-parametric methods.（2）This paper establishes a CNN-based option pricing model.The pattern recognition mechanism is used to extract option comovements when using CNN to estimate the prices.In addition,this paper proposes a feature rearrangement convolutional neural network（FR-CNN）model to tackle problem of the comovements among all the options.This paper conducts empirical analysis and research based on the 50ETF option.The classic BSM,SV and JD models are used to compare and analyze the pricing results obtained by the non-parametric CNN and FR-CNN models.（3）Parametric and non-parametric models are integrated based on the idea of ensembling algorithms.Parametric and non-parametric methods have their own advantages and disadvantages.Based on the idea of stacking integration algorithm,this paper constructs a CNN based ensembling（CBE）with CNN method as meta-learner.Based on the boosting integration algorithm,this paper proposes residual boosting ensembling（RBE）.By using the CBE and RBE methods,the parametric and non-parametric models are integrated to avoid errors caused by selecting one single model.Using the SSE 50ETF option to test the option pricing system based on non-parametric methods that take into account media news information,the analysis results can be drawn as follows:（1）Compared with the basic input combination that only considers five fundamental factors,considering additional input variables including historical transaction variables and news variables will significantly reduce the pricing error of non-parametric models.Furthermore,on the basis of five-factor input,considering additional news factors will result in slightly more efficient results than considering historical trading variables which further proves the effectiveness of considering news sentiment in option pricing.（2）FR-CNN and CNN can obtain better pricing effect than the parametric model considering the effects of transaction variables and news variables,indicating the effectiveness of the non-parametric option pricing model.In addition,using the FR-CNN model to price options can get better results than the CNN model,indicating that the method of feature rearrangement for option pricing can well consider the generality among different strike price options.However,due to the advantages and disadvantages of non-parametric and parametric models,parametric models can get better pricing results for options under certain moneyness and time to maturity categories.（3）The integration algorithm based on stacking can obtain more effective results than the single parametric model.The classic SAM and LSE algorithms can obtain better results than single parametric model,but cannot obtain more effective results than the non-parametric FR-CNN model.The CBE integrated model with CNN as the meta learner can get better results than any single parametric model and non-parametric model.Three ensembling model including RBEJD,RBECN,and RBEFR perform better than any single model after residual calibration.Among them RBEFR obtains the best results. |
