In the ever-changing financial market, the steady investment is always expected and praised by people. Based on the method of statistical arbitrage, quantitative hedge fund established in European and American markets can obtain stable arbitrage profit every year. With the launch of stock index futures and securities margin trading, statistical arbitrage is poised for growth in China. Introducing and analyzing the common models and methods of statistical arbitrage, this dissertation aims to compare the profit and risk of different transaction objects under different arbitrage models.The models used in this dissertation are based on two kinds of assumptions. One adopts the cointegration arbitrage model on the basis of assets variables linear assumption. The other adopts Copula arbitrage model on the basis of nonlinear assumption. It also discusses the profit and risk of calendar spread arbitrage, intercommodity arbitrage, cross-time arbitrage and stock arbitrage under these two models. By empirical research, we can draw the following conclusions:By empirically analyzing this month contract and next month contract of Shanghai and Shenzhen 300 stock index futures under the cointegration arbitrage model, it comes to a conclusion that the option of widow phase and the setting of threshold value have a great effect on transaction results. By exploring, it also finds that the effect of one-day transaction session is best when it has every five minutes high-frequency transaction data and three-days modeling time. Also, the open threshold value is best when it is between 0.5 time standard deviation and 1 time standard deviation. It is almost consistent with the result of the best transaction signal based on the process of O-U in the following.We assumed that each investment is delta, and unrepeated use, to discuss the fluctuation of each arbitrage returns. We found the profit based on the Copula arbitrage model is unstable and fluctuant, even it appears the phenomenon of accumulated profit loss. At the same time, we design an optimization scheme, namely, we build a position by choosing a better position than the previous one among real-time data, which can reduce the rate of accumulated profit, control risk and decrease the magnitude of accumulated profit loss. We also assumed the initial investment is unit one, and repeated used daily, and calculated the cumulative yield rate by the method of compound interest, the finally result shows that which higher than the bank deposit rate of return.In the horizontal comparison of different transaction objects, calendar spread arbitrage, inter-commodity arbitrage and stock arbitrage under the cointegration arbitrage model can achieve good arbitrage profit. Among them, the cumulative yield rate of stock accumulated arbitrage is at 67.43%.Among them, the profit of stock accumulated cointegration arbitrage is at 67.52% which is the highest. While cross-time arbitrage under the cointegration model is hard to obtain arbitrage profit. All transaction objects can gain relatively stable profit under the Clayton-Copula and Gumbel-Copula model. Especially, the cumulative yield rate of stock accumulated arbitrage under Clayton-Copula is at 77.32%, which is higher than the others. Which demonstrates there is great arbitrage space in Chinese stock market. It is also important to note that different transaction objects should have its own optimal arbitrage model and method, and one arbitrage model is not universally applicable. In addition, through the optimization of the Copula arbitrage model, the cumulative annual yield of all of the arbitrage transaction objects have increased significantly. |