The Calendar Spread Arbitrage Of Stock Index Futures Based On Statistical Arbitrage Theory

Stock index futures are the product of the development of modern capital markets. In the 1970s, Western countries affected by the oil crisis, economic development is very unstable. Interest rate fluctuations lead to fluctuations in stock prices, stock investors urgently need a way to mitigate risk. As a result, stock index futures came into being. After several years of development, stock index futures has become the world's most active investment products.The arbitrage of stock index futures play very important role in making the price of stock index futures to be rational and activate the market. It can make the function of stock index futures market to be exert fluently. In this paper, we take the launch of stock index future market of our country as research background, use thought of statistical arbitrage to investigate calendar spread arbitrage of stock index future.In this paper we select recent month consecutive contract and next month consecutive contract's high frequency data as study object. First test the co-integration relationship between this two contracts, and the outcome show that, there is co-integration relationship between each other. Then based on the theory of cost of carry model, we tested the relationship between risk-free interest rate and dividend yield, and outcome show that, cost of carry model can explain thirty five percent of spread between recent month contract and next month contract. Then conducted a Granger causality test and error correction tests, the results show next month consecutive contract was the Granger causality of recent month consecutive contract.The statistical arbitrage are based on mean reversion, but the change of economic environment led to the central of mean-reversion change, Therefore, in order to portray this feature, in the paper, we use weighted moving average to depict it. Meanwhile, the spread sequence also showed the characteristics of heteroscedasticity, so we use garch model and exponentially weighted moving average to depict it. After determining the mean and variance of spread, the article use normal distribution to describe the distribution of spread, and base on this distribution, we constructed a spread arbitrage model.Finally, article use the data of stock index futures market to tested the arbitrage effect of statistical arbitrage model, and the outcome show that the statistical arbitrage model can make stable revenue.