A Hybrid Neural Network Option Pricing Model Based On Option Investor Sentiment And Limits Of Arbitrage

Since the research of Black,Scholes and Merton,there has been a proliferation of improved models introducing parameters such as jumps,stochastic interest rates,and stochastic volatility to better characterize the heavy tails of financial assets and explain market anomalies.The advantages of these structured parametric option pricing models are their economic intuitiveness and rich economic implications,but the disadvantage is that they are based on strict assumptions,lack flexibility,and have complex models that are not easily handled.On the one hand,In recent years,with the development of computer and artificial intelligence,especially for the acquisition and application of big data,it makes various methods relying on data mining become popular.There have been many scholars who have used machine learning or deep learning to price options,and these data-driven nonparametric option pricing models are flexible and easy to handle,but lack economic explanations.Hybrid neural network is an integrated model that takes into account the advantages of both and has received extensive attention and research in option pricing models.On the other hand,investor sentiment is a systematic risk affecting the equilibrium price of financial assets,as many scholars have empirically shown to be the case in the options market as well,and this effect is further amplified by the limits of arbitrage in the underlying market.Considering the impact of these two factors on option prices,this dissertation introduces investor sentiment and limits of arbitrage into a hybrid neural network to investigate the option pricing problem.First,for the structured parametric model part in the hybrid neural network,this paper introduces both the stochastic interest rate and the mixed exponential jump into the model based on the Heston model.And taking into account the fact that there is already negative interest rate in the financial market,this paper tries to relax the restriction that interest rate cannot be negative,assuming that it satisfies the Hull-White process which is different from the classical CIR hypothesis.Finally,the HHM model is proposed.In terms of model solving,this paper adopts the fast Fourier transform(FFT)method to obtain the semi-closed solution of pricing containing the characteristic function of logarithmic price.The results of numerical analysis show that the structured parametric model proposed in this paper captures the market characteristics well,such as heavy tail,leverage effect,profit and loss asymmetry,etc,and implied volatility surface patterns.Second,this paper constructs two key feature variables that are input to the hybrid neural network: options investor sentiment and the degree of arbitrage limits.Daily option investor sentiment indicators are constructed based on the option turn volume,open interest,turnover rate,put/call ratio,underlying historical volatility,and Baidu index of option; the difference calculated by the option put-call parity(PCP)is used to measure the limits of arbitrage.Based on this,this paper designs the architecture of feedforward neural network,a data-driven nonparametric model component,discusses the integration of hybrid neural networks,and gives the full pricing process of the hybrid neural network option pricing model considering investor sentiment and limits of arbitrage.Finally,this paper uses data related to the options market of SSE 50 ETF and applies the improved hybrid neural network model proposed in this paper for empirical analysis.The process is: 1)obtaining all the required data,including SSE 50 ETF option contract and trading statistics,its underlying Huaxia SSE 50 ETF fund data,Baidu index,etc.; 2)parameter calibration of the HHM model,and calculating the HHM model price and pricing error by FFT; 3)calculating the option investor sentiment indicator and the degree of arbitrage limits indicator in the sample period; 4)using hybrid neural network for learning and forecasting.And the pricing accuracy of the model is measured by MAPE and RMSE indicators; 5)robustness testing,comparing with other 9 option pricing models,and analyzing the results.The final empirical results show the model proposed in this paper can better capture pricing error and has greater pricing accuracy than models that do not consider or consider only a single factor.