Copula Theory And Its Applications In The Financial Analysis

With the development of the financial markets, the dependent relationship between them become more and more complicated and represent nonlinear, asymmetric and tail dependence. Methods based on the linear correlation coefficients can not describe the dependence pattern accurately. Sklar's theory of copulas believe that the information about the dependence is whole contained in the copula function. In this dissertation, we research the dependence pattern of the financial markets by using copula function, and probe into some theory question of the copula and its application in financial analysis.Definition and some basic property and some related theory of copulas are introduced, dependent characters of some common copula are analyzed. Several measures of dependence educed by copula function is analyzed inside out, these measures can catch non-linear and tail dependent dependence. Several copula parameter estimate methods are summarized. Because marginal distribution function must be assumed when use MLE and the stepwise methods, which apt to cause mistake parameter estimation of copula. However, quasi maxi-likelihood estimation methods only require empirical distribution transformation, and can estimate the parameter of Copula more accurately.For copulas which satisfy certain condition, we construct two statistics.Based on the statistics, goodness fit of tests for copulas are conducted. Moreover, power of the tests is researched by using simulation methods. The comparative study with some other methods of tests is carried in term of power of tests. The result indicates that, under certain situation, the method put forward in the dissertation is superior to some existing methods of tests.In research of application, copulas are applied to the financial market dependent analysis, Value-at-risk calculation and portfolio selection. The empirical results getting from Shanghai stock markets and Shenzheng stock markets show that the mixed Gumbel copula we constructed can describe the asymmetrical tail dependence. Copula-GARCH-GPD model is build up, and used in portfolio selection based on CRRA and simulation methods. The finding of dependence of European dollar and pound sterling is that gs Copula-GARCH-GPD can portray the dependent pattern of the two exchange rate better, and so can win higher accumulative yield. Finally, semi-parametric Archimedean copula family have a flexible dependence structure, the positive research of the foreign exchange market indicates this Copula can describe self-adaptively the dependent information included in the data.