Research On Minimum Variance Delta Hedging Theory Based On LSTM Neural Network

From 2007 to 2009,U.S.stock options showed a trend of rapid growth,becoming the option product with the largest trading volume,followed by ETF options.The listing of Shanghai 50ETF index options means that the era of Standardized Options Trading in China has officially opened.Globally,option took gradually significant function in risk control.On the one hand,options can be used to mitigate risk exposures caused by changes in the price of the underlying asset;on the other hand,they can also be applied specifically to mitigate risks due to volatility.Delta is by far the most important hedging parameter,and Delta is also the easiest parameter to adjust,because it only needs to trade the underlying asset.Based on the Black-Scholes model,Delta played an important role in hedging.Option traders reduce their risk exposure by frequently adjusting Delta to near zero.It is just because of the negative association of underlying assets prices and the volatility that did not give the underlying stock position that minimizes the Variance of the hedger's position.Hull and white(1987),Heston(1993)and Hagan(2002)have proved that if Delta is calculated as the partial derivative of option price relative to asset price,the hedging effect is obviously different from the actual situation.The Minimum Variance Delta mainly considers the impact of changes in the underlying stock price and volatility expectations based on changes in the underlying stock price.Bakshi(2000)examined the S?P 500 index call options from September 1993 to August 1995;Alexander et al.(2009)also compared and analyzed the hedging performance of six different models for call and put options in the S?P index trading in 2007,and found that changing the Delta in the general sense into the Minimum Variance Delta would improve the performance of Delta hedging.This paper mainly based on the domestic Shanghai 50ETF index option data and Shibor interest rate data from the beginning of 2016 to the end of 2019.The full text is interspersed through the comparison of the two lines.The first line is the comparison of prediction ability between nonlinear fitting prediction model and linear fitting prediction model.The second line is within the LSTM neural network to compare the prediction ability between modular LSTM and non-modular LSTM on the basis of the differences between the features like moneyness and time to maturity.Finally,the Minimum Variance Delta predicted by the three models is applied in the framework of Leland hedging strategy which constructed to compare and analyze the variance and total profit and loss of daily change of traders' position value.Through the empirical analysis of double line comparison,it is found that:(1)Nonlinear LSTM neural network has more advantages in fitting implied volatility.Because the domestic options market is not mature,the market data of Shanghai 50ETF index options is not perfect,but the strictness of LSTM neural network for data is not as high as linear model.Meanwhile,the special forgetting mechanism of LSTM makes its processing of time series data better,and it can keep the history information for the series data,so that the model can train and learn the data more fully.(2)By comparing the effectiveness of hedging percentage,it is found that LSTM neural network has higher effectiveness.It shows that the Minimum Variance Delta predicted by LSTM neural network can more effectively explain the negative impact of hedging caused by volatility changes.(3)In the first exam of LSTM neural network,it is found that modular neural networks are sufficient to summarize data in the same module,so the model can learn more relevant characteristics and has a positive effect on the prediction in the module.The advantage is that the modular LSTM is more accurate in both the loss function and the final Minimum Variance Delta fitting.However,through analysis and research,it is found that the operation efficiency of modular LSTM is lower,because it needs to implement redundant training steps for each module,and the higher accuracy is obtained on the basis of the loss of operation efficiency.Therefore,combined with the actual situation,it is a compromise proposal between the operation efficiency and the prediction accuracy.(4)By applying the Minimum Variance Delta predicted by the three models to hedging strategy,the effectiveness of the Minimum Variance Delta theory in Shanghai 50ETF index options is verified.The Minimum Variance Delta has a higher effect on controlling the variance of the value change of the traders' position and the total profit and loss,which indicates that the Minimum Variance Delta hedging can more significantly mitigate the negative impact of the negative correlation between the volatility and the price of the subject matter on the hedging.The innovation is discussed in the following parts including theory,modeling and applications:(1)LSTM neural network model is used to predict the implied volatility.The excellent ability of LSTM neural network for data learning is more suitable for the domestic immature option market,and the corresponding forgetting mechanism is also more suitable for time series data.(2)In the calculation of Minimum Variance Delta,the slope of volatility skew is added to replace the derivative of implied volatility to the price of the underlying goods.Combined with the volatility characteristics of real market,the conversion from implied volatility to Minimum Variance Delta is realized.(3)Through the establishment of fixed time interval Delta hedging strategy,this paper verifies the effectiveness of Minimum Variance Delta hedging in Shanghai 50ETF index options,polishes the application of Minimum Variance Delta hedging theory,and increases the feasibility of Shanghai 50ETF index options risk management.Inevitably,due to the limited research level,shortages are obvious to some degree:(1)The Minimum Variance Delta hedging strategy is limited to Leland hedging.The structure of hedging strategy is relatively single.As for the empirical process,it generally deals with the hedging problem of call option and put option,while,does not distinguish the hedging gap of related options in detail.(2)As for the prediction of LSTM neural network,I only deal with the data in modules,and do not carefully split the network structure and forgetting mechanism of LSTM neural network.