Pair-Copula Constructions Of Multiple Dependence And Its Application

With the development of the financial markets,the dependent relationship between financial assets become more and more complicated and represent nonlinear, asymmetric and tail dependence,as well.Methods based on the traditional linear correlation coefficients can not describe the dependence pattern accurately.SKlar's theory on copulas believes that the information about the dependence of random valuables is wholly contained in the copula function.Hence,most researches home and abroad start to use different copula functions to describe the relation pattern of random valuables,who do not consider the fact that it is possible that random both valuables gotten from multiple random valuables do not have the same distribution, resulting in different copula functions.Based on such the fault,this article introduces a new method—pair-copula,which allows to apply different copula functions that are to describe relationships among random valuables more accurately,and that are also to build the density functions of joint distributions which simplify the process of parameters' estimations.This article first introduces the basic principle and main methods about VaR which include analysis method,historical simulation and Monte Carlo simulation. Then,it presents basic principles of copula,including its characteristics and features. The family of ellipses and Archimedes are also presented,plus the problem of how to measure the relationship of valuables.Following with it is the method of pair-copula. In this section,it first introduces some common methods to build the copula functions among multiple random valuables including their respective faults.Then it presents all knowledge about pair-copula such as the process of parameters' estimations and how to test its goodness of fit,which will be used in the next section.Later,it talks about the application of pair-copula.It is based on three China's stock markets' interest and the result is also tested by goodness of fit and VaR,which obtains good result.The final part of this article is the summary and some parts needed to improve.