Mixed Copula Function And Its Application In Finantial Analysis

Correlation analysis is the hot and difficult point in the modernfinancial analysis, measuring the relationships among financial marketsaccurately is the necessary premise of analyzing financial problems. Withthe accelerated process of global integration, the related structures amongfinancial markets become more complicated, and the related patternsamong financial markets show nonlinear﹑asymmetric and tail dependentfeatures. As a tool of multivariate statistic and correlation analysis, theCopula function can describe the related structures among financialvariables robustly and practically, but a single Copula function can onlyreflect indirectly the correlation among financial markets. If we want tofully understand the related structures among financial markets, it is verynecessary to construct a more flexible Copula function-mixedCopula model. Mixed Copula function has many excellent properties thata single Copula function does not have, and it not only highlights thecharacteristics of a single component Copula function，it also covers themixed characteristics of these component Copula functions.For the sake of simplicity, I take bivariate mixed Copula function as an example and try to do several work of the following aspects in thispaper.1The relationship between correlation measurement based on mixedCopula function and correlation measurement based on these componentCopula functions are discussed; The synthesis method is given to producerandom number of a mixed Copula function, and we discover that thealgorithm is effective by the simulation.2We adopt nonparametric kernel density estimation method to estimatethe financial asset return distribution; The process of the parameterestimation method of mixed Copula function is deduced by EM algorithmand L-BFGS-B algorithm, and the R code of the parameter estimationmethod of mixed Copula function is writed.3The linear combination of Clayton、Gumbel and Frank Copulafunction is used to construct mixed Copula function, we draw aconclusion that based on mixed Copula function, the related structurebetween the Shanghai composite index and the Shenzhen componentindex is the most accurate and flexible.4The mixed Copula-VaR model is put forword, we draw a conclusionthat based on mixed Copula function, the VaR of the equal weightcombination between the Shanghai composite index and the Shenzhencomponent index is the most reasonable and accurate.Finally, we summarize and analyze the work of this paper, and show the topic of further study.