Research On Some Quantitative Trading Problems In The Framework Of Stationary Process

As we all know,the law of large numbers provides" free lunch" for many industries,such as casinos and insurance.In the field of quantitative trading,the law is also an important magic weapon for statistical arbitrage strategy to obtain long-term stable profits.However,due to the inevitable strong correlation between financial data,the premise of independence can not be met.Therefore,we need to find a theoretical support beyond the law of large numbers:stationary process.Professor Zheng Wei'an established a set of statistical arbitrage theory and method based on stationary process by making full use of ergodicity theorem,an excellent property of stationary process.This paper will learn from the research ideas and framework,try to further explore the different statistical arbitrage opportunities in commodity futures market,stock index option market and stock market,in order to obtain stable returns.This paper is divided into three partsFirstly,the third chapter studies the high frequency statistical arbitrage strategy in commodity futures market.Zheng and Wang[104]developed a series of single factor high frequency statistical arbitrage strategies which can make stable profits in the Shanghai and Shenzhen 300 stock index futures market under the framework of stable logarithmic increment of asset prices.After the stock market crash in September 2015,with the increase of handling charges and margin,as well as the restrictions on the number of intraday trading,more and more institutional investors focus on the high-frequency trading of commodity futures.Through a large number of data studies,it is found that the hypothesis that the logarithmic increment of asset price is a stationary process still holds in several types of commodity futures,which also provides the possibility of high-frequency statistical arbitrage in commodity futures market based on the stationary process.According to the characteristics of commodity futures market,this paper proposes a multi factor high frequency statistical arbitrage strategy based on stationary process.The back test results show that the multi factor high frequency statistical arbitrage strategy can obtain stable returns.With the continuous progress of computer technology and data storage capacity,how to integrate higher dimensional stabilization factor into high-frequency trading has become an urgent new problem.To solve this problem,this paper proposes the theory and method of factor promotion in the framework of stationary process.The empirical part takes the classic boll strategy as the background of promotion,and illustrates the effectiveness of the promotion strategy through different cases.Then,the fourth chapter studies the statistical arbitrage strategy in the stock index option market.Zheng and Bao[2]found that the risk neutral pricing method of financial derivatives based on the efficient market hypothesis ignores the objective fact that the stock index has a long-term value of ?>r>0.In this paper,we first prove that the theory of stationary stock index option statistical arbitrage is still valid under the stochastic volatility model.Aiming at the deficiency of basic strategy in the face of black swan event,this paper proposes a stationary option statistical arbitrage enhancement strategy with dynamic hedging,so as to effectively offset the market crash risk caused by continuous put selling.Considering that the basic strategy needs to hold a large number of short positions of put options,but due to financial supervision,the short positions of put options held by large institutions are strictly limited,so the basic strategy is not suitable for institutions with large amount of funds.In order to solve this problem,based on Zheng and Bao's[2]statistical arbitrage idea of stock index options,this paper proposes a new statistical arbitrage strategy of stabilized covered call options.Through the back testing of the actual data of qqq,DIA and spy stock index options in the United States,it is found that under the same leverage level,the statistical arbitrage strategy of stabilized covered call options is better than the basic strategy in the return risk ratio This is consistent with the theoretical derivation.Finally,we extend the principle of stationary statistical arbitrage of stock index options,and design a statistical arbitrage strategy that can be applied to China's Shanghai Stock Exchange 50 ETF option market.Finally,the fifth chapter studies the strategy of similarity shape matching in stock market.In this paper,we first use the MF-DFA method in statistical physics to verify that in most stock markets,the return series have fractal properties,that is,the history can be repeated.Then,under this assumption,the dynamic time warping DTW algorithm,which is commonly used in speech recognition technology,is used to find the n most similar technical forms in the historical database.If one of the N technical forms is significantly unbalanced,the current trend will be judged as the technical form.In the back testing part,considering that many scholars used to analyze the occurrence of each technology form as a series of independent events,this paper analyzes the forecasting ability of technology form to stock price from the perspective of strategy.Finally,the stationary step spa test is used to test the effectiveness of the constructed stationary morphological recognition strategy.Back testing found that:the predictive power of technical form in medium market value samples is higher than that in large market value samples.The whole analysis framework also provides a new idea for the study of financial events in quantitative trading.