Research On The Hedging Model Of Mixed Copula-GARCH-CVaR Non-ferrous Metal Futures Based On PSO Optimization

In recent years,the price of China’s non-ferrous metal market has changed greatly,which makes non-ferrous metal related enterprises urgently need to deal with the risk from the price fluctuation of raw materials.Commodity futures has the function of transferring risks.Enterprises or investors can hedge by establishing short or long positions in the futures market to resolve price risks in time,and the effectiveness of hedging mainly depends on the accuracy of the optimal hedging ratio adopted by enterprises.The hedging model based on CVaR method can use the setting of confidence level to meet the needs of enterprises or investors with different risk preferences,but it usually uses linear correlation coefficient to measure the correlation between futures and spot market.The existing research results point out that when the futures and spot market prices have great volatility,the correlation between futures and spot prices is no longer linear,and the conventional linear correlation model can not accurately describe the correlation between them.Aiming at this problem,this study will build a variety of copula models to fit the data of futures and spot,and obtain the nonlinear correlation coefficient between them,so as to replace the linear correlation coefficient in the traditional hedging model.Firstly,the GARCH family model is used to fit the volatility of Shanghai aluminum spot and futures prices,and the specific marginal distribution is determined as student t distribution according to the actual situation of fitting;Secondly,the Mixed Copula model is constructed,and all unknown parameters of the Mixed Copula model are solved by maximum likelihood estimation method combined with exponential inertia weight particle swarm optimization algorithm,so as to more accurately describe the asymmetric and nonlinear correlation between Shanghai aluminum spot and futures;Then,under the goal of minimizing CVaR,a Mixed Copula GARCH CVaR model based on PSO optimization is constructed,and the hedging ratio of Shanghai aluminum futures is calculated on this basis;Finally,the model is compared with Clayton Copula GARCH CVaR hedging model,Gumbel Copula GARCH CVaR hedging model and frank Copula GARCH CVaR hedging model.The results show that:(1)compared with the single copula model,the Mixed Copula model optimized by PSO can better describe the correlation between non-ferrous metal Shanghai aluminum futures and spot market.Specifically,there is a greater asymmetry between Shanghai aluminum futures and spot market,and the upper tail correlation is stronger than the lower tail correlation,It shows that when the price of Shanghai aluminum futures rises due to the large fluctuation in the non-ferrous metal market,the probability of the spot price rising is large;(2)Under different confidence levels,whether from the perspective of risk alone or from the perspective of unit risk return taking into account risk and return,the Mixed Copula GARCH CVaR model based on PSO optimization constructed in this paper shows better hedging effectiveness than other models.