Symmetric Bernstein Copula

In many fields of finance, such as Stock, Portfolio and Exchange Rate, inorder to reduce the risk, investors usually invest in some portfolios. The depen-dence among the portfolios is the key factor to reduce or disperse the financialrisk. Because of its special properties, Copula is broadly applied to describe thedependent structure. The famous theory , Sklar theory, shows that any jointdistribution can be divided into marginal distributions and dependent structure,i.e. Copula. Rescently, more and more papers use Copula to fit the dependentstructure among portfolios,but the Copulas they used are usually one parameterfamilies. With portfolios being more diverse, the complexity of dependent struc-ture is higher and higher, one parameter Copulas have already couldn't describethe dependent structure among portfolios suffciently.Bernstein Copula, which is in form of multinomial, is one of the multiple pa-rameters Copulas. So far, some papers have used it to fit the dependent structureamong portfolios. This paper which is based on Bernstein Copula, puts forwardand defines the Symmetric Bernstein Copula, provides its basic properties in theform of theory. When the dependent structure among portfolios is fairly symmet-ric, this paper shows some advantages compared with Bernstein Copula and oneparameter Copulas theoretically, it also demonstrates that the fitness of SymmetricBernstein Copula is better than other Copulas.