Research On Stock Arbitrage Strategy Based On GARCH Model And Copula-OU Proces

In recent years,with the outbreak of the epidemic,the transformation between bull market and bear market in China’s A-share market is not obvious,but has been in a state of shock.If investors want to obtain stable investment income in the shock market,they need to learn to use statistical arbitrage strategy to reasonably avoid risks.In this context,this paper uses GARCH model and copula function to construct transaction signals,and introduces MCMC algorithm and OU process to improve the two transaction signal construction methods respectively,so as to improve the market fit of transaction signals and provide suggestions for investors to write statistical arbitrage strategies.Firstly,this paper selects the stock pairs with strong correlation from CSI 300.Secondly,different arbitrage schemes are designed based on GARCH model and copula function respectively: For GARCH model strategy,the cointegration regression equation of two stocks is established,and the trading proportion of two stocks is determined according to the regression coefficient.Considering the heteroscedasticity of residuals,the trading signal is established by GARCH model,and the model parameters are optimized by MCMC algorithm;For the copula function strategy,firstly,the ARMA-GARCH model is used to fit the edge distribution of the stock return series,then the appropriate copula function is selected for parameter estimation,the conditional probability is obtained,the trading signal is established,and the OU process is introduced to process the trading signal series with mean recovery characteristics,and the approximate solution of the opening line under the optimization of the expected return function is calculated.Finally,according to the arbitrage strategy designed above,the data of one year outside the sample are used for back testing,and the indexes such as sharp rate,maximum pullback and yield are calculated.Compared with the traditional cointegration strategy,the income effects of the two strategies are analyzed.The empirical results show that: 1.Different arbitrage strategies can exceed the return of individual stocks in the sample,and can effectively reduce the investment risk.The back-test results outside the sample also show that statistical arbitrage is feasible in the A-share market;2.Compared with the traditional ML estimation method,the GARCH model optimized based on MCMC method can more accurately reflect the fluctuation risk of spread series,create a time-varying trading threshold through time-varying standard deviation,broaden the trading range,make the stop loss signal more accurate,and better reduce the trading risk.Therefore,GARCH model strategy has better performance than traditional cointegration strategy in terms of yield,trading times and sharp ratio;3.Compared with the traditional cointegration strategy and GARCH model strategy,the arbitrage strategy based on Copula-OU process can make full use of the nonlinear related information between the two stocks,capture the slight deviation of the price difference caused by market emergencies more keenly,the back test effect is more lasting,and has stronger robustness,which can provide a basis for the optimization of stock arbitrage strategy.