The Application Of Mixture-Copula Method In Statistical Arbitrage

Since the 19th CPC National Congress,higher requirements have been put forward for the development of capital market.In 2018,the financial work conference emphasized to adhere to the new concept of development,to protect the legitimate rights and interests of investors as the fundamental mission,to serve the real economy,guard against risks and deepen the reform of the three major tasks.In this context,the paper will study the application of Mixture-Copula in statistical arbitrage.Copula has made great progress in basic theory,making it possible to study financial risks.Copula theory can capture the weak correlation between variables well.Weak correlation reflects the risk of financial market,and it can effectively warn risks.As a quantitative strategy,statistical arbitrage makes capital market transactions more rational and is a protection for investors.So the topic of the paper has the value of application.Firstly,the general theory of Copula method is combed,and the characteristics of Copula function are studied in detail.Theoretically,it has made necessary preparations for the Copula function to study the financial market.Based on this,we study the Mixture-Copula function in depth.In this process,a new algorithm is introduced to optimize the parameter estimation method of Mixture-Copula model.The simulation experiments are completed under different composition function of Mixture-Copula.The experimental results show that the new algorithm can effectively improve the accuracy of parameter estimation.Then,the paper analyzes the statistical arbitrage theory and the commonly used arbitrage strategy,and understands that the traditional arbitrage method does not capture the nonlinear non symmetric variable relations,and the connection function method can be improved in this respect.In order to solve the problem of risk measurement,the paper builds statistical arbitrage model based on Mixture-Copula function,so as to get the corresponding trading strategy.Combined with the actual data of bank sector stock,the arbitrage model and the unilateral arbitrage model are analyzed.The results show that the strategy is feasible.The innovation of the paper is reflected in the following aspects:Firstly,build a unilateral statistical arbitrage model based on Mixture-Copula.The maximum likelihood estimation method based on the Mixture-Copula function model is improved,the EM algorithm is introduced and the parameter estimation method is optimized with the LBFGS algorithm to reduce the complexity of the parameter estimation.Secondly,the traditional statistical arbitrage strategy has been improved to capture the weak correlation of the tail more accurately,which improves the income range.In addition.the application of the unilateral model provides a new way of thinking for the majority of the traders who do not have the qualification of margin financing in the stock market,and has a certain application value for the research of the innovative arbitrage strategy.