A Study On ETF Option Pricing Based On Wiener-Itō Chaos Expansion And Generative Adversarial Networks

Since 2020,the impact of the new crown pneumonia epidemic has led to drastic fluctuations in the financial market,and options,as an effective tool for transferring market risk and hedging,have become the best choice for investors to hedge market risk.Foreign option market has been developed for a long time,with mature pricing mechanism and stable trading environment;domestic option market has been developed for a shorter period of time,lacks sound pricing mechanism,and the trading environment still has much room for improvement.How to develop China’s options trading market and how to better use options tools to improve the market’s risk management capabilities are important issues to be addressed in China’s financial market in the future.In order to give full play to the role of options in risk management,asset allocation and price discovery,efficient and reasonable option pricing is the foundation.In this paper,we take the call option of 2019 SSE 50 ETF as the empirical research object,and build the option price prediction model based on Wiener-Itō chaos expansion(WIC)and Generative Adversarial Networks(GANs)under the Heston model.Firstly,in response to the inability of the traditional Black-Scholes pricing model to explain the essence of the smiling volatility curve in the market,the Heston option pricing model,a representative of stochastic volatility model,is introduced as the underlying model;secondly,in response to the problem that the global optimization algorithm in the parameter estimation method of the Heston model is not stable enough and the local optimization algorithm is easy to fall into local Second,to address the problems of the Heston model parameter estimation method,the global optimization algorithm is not stable enough and the local optimization algorithm is easy to fall into local minimum,this paper combines the simulated annealing algorithm with the nonlinear least squares(lsqnonlin)algorithm,firstly,the optimization parameters are obtained by the simulated annealing algorithm,then input as the initial parameters into the lsqnonlin algorithm to solve,if the loss value decreases,the optimization parameters are updated,otherwise,the previous parameter solution is retained;again,because the pricing model tends to be complicated,it is difficult to find the closed form The paper derives an approximate pricing formula for the European call option under the hybrid volatility model based on the WIC method,and brings in the parameter solution obtained in the previous step to obtain an approximate value of the option price under the Heston model,and then obtains the difference D between the approximate value and the actual value;then,because the traditional parametric model cannot effectively analyze the high-dimensional and noisy financial data,the paper introduces Generative Adversarial Networks(GANs)are used to construct generators and Multilayer Perceptrons(MLP)to construct discriminators using Long and Short-term Memory Networks(LSTM).Unlike previous studies where the machine learning algorithm is directly used to train the option value C,this paper uses the machine learning algorithm to train the difference D.The predicted value of the difference D is summed with the option price approximation to obtain the predicted value of the option price;finally,the model effect is evaluated by three average error indicators:Mean Square Error(MSE),Mean Absolute Error(MAE),Mean Absolute Percentage Error(MAPE)Finally,six comparison models were designed for comparative analysis.Combining the 3 evaluation indicators,the following conclusions were obtained.First,the prediction effect of this paper is optimal,and the prediction effect is better when training based on larger samples;second,the idea of using machine learning methods to train the difference D is better than that of directly training the option price C in terms of prediction accuracy and prediction stability;third,the GANs algorithm built with LSTM as the generator and MLP as the discriminator is better than that of training the difference D or training the option price C.Fourth,the prediction accuracy and prediction stability of the Heston model are slightly worse than those of the nonparametric machine learning model,which reflects that the machine learning algorithm performs better in analyzing financial data.Innovation points of this paper: on the one hand,this paper combines the WIC method with the GANs model,uses the approximate option pricing formula derived from the WIC method to find the difference D under the Heston model,introduces the GANs model constructed with LSTM as the generator and MLP as the discriminator to train the difference D,conducts an empirical study on the SSE 50 ETF options,and conducts a comparative analysis with the prediction effect of the comparison model;on the other hand,this paper organically combines the simulated annealing algorithm with the lsqnonlin algorithm to accurately estimate the parameters of the Heston model.