Pairs Trading Strategy Based On Copula Function

At the end of the last century, all the securities business and investors in Europe and the United States market using statistical arbitrage created brilliant investment performance. Prior to2010, short mechanism has been lacking in our country, which has seriously hindered the pace of the development of quantitative investment strategies.The introduction of margin trading and securities lending business, especially the listing of stock index futures had dragged the domestic market out of the dilemma. Many asset management institutions and scholars began to pay attention to and study statistical arbitrage. So, in recent years, statistical arbitrage has experienced an alarming development in China’s financial market.By normative analysis, this paper analyzes the effectiveness of the market in the first, and then introduce the basic theory of strategy, all preparations are ready toconstruct the strategy, Finally, compare the various policies through empirical analysis, this paper comes to useful conclusions step by step.Theme of this article is such a idea:after deeply studying the pairs trading strategy based on the cointegration theory which many researchers and traders familiar,we find this strategy exists serious defect. it can only characterize linear correlation between random variables or market,while can’t describe some increasingly prominent non-linear models,such as asymmetry, progressive tail-related or independent mode. With the rapid development of financial markets, cointegration theory is obviously not enough, because it can’t completely depict dependence relationship between random variables, and thus missed many trading opportunities, this paper attempts to introduce Copula function in this case, the family of Copula function has a great many advantages, so they can compensate for the lack of cointegration in a certain extent.Specifically, this paper can be divided into two blocks:The first part briefly describes the various theories, laid the foundation for building strategies. Firstly,introduces the concept of statistical arbitrage, summarizes the currently commonly used pairs trading strategy. Then introduces Copula theory, including the definition of Copula functions, basic properties, and measurement methods associated with correlation, etc. It also summarizes and compares the common type of Copula functions. Only we understand the characteristics of each Copula functions,can we build mixed Copula function better in later.The second part involves the construction of strategies and empirical analysis. Initially, On the basis of other scholars research,we choose the most appropriate connection function from a number of Copula function after selecting and estimated Copula function to connect the edge of the distribution function to get the joint distribution. Then define an indicator as trading signals, this indicator is essentially a conditional distribution,it can be used to indicate the decline probability of the yield rete of one species repect to another species. Supplemented by other trading rules,we build a pairs trading strategy based on a single Copula function. In the process of building, we found a single Copula function is still not enough to described the dependencies between random variables completely,so we have ideas for improvement Copula function,use mixed Copula function which is the linear combination of several single one to build a new pairs trading strategy,the reason is that the linear combination of Copula function is still Copula function,it does not change the good nature of Copula function.The empirical part use kendall’s rank correlation coefficient to choose out of the two varieties,rubber and PTA,from all the commodity futures,then use these two varieties empirical analysis the two pairs trading strategies based on Copula theory,and compare them with co-integration strategies.Finally, the conclusion is that the three methods can profit, but the annual yield of co-integration strategy is significantly lower.The highest annual rate of return is the strategy based on mixed Copula function. This result is in line with expectations.This paper aims to provide a new perspective to study pairs trading strategy for researchers and traders.