The Dependence Model And Its Applictions Of Financial Risks Based On Copula Theory

Modeling dependence between time series in financial risk management field is of key importance to portfolio diversification, international asset pricing, contagion of volatility and risk management. It is insufficient to only consider the degree of dependence between random variables in establishing risk management models, and we must still consider the structure of dependence of them. In this paper, based on the characteristic of financial time series volatility, several copula-based models are established to study the dependence structure between financial time series, and applied to analyse the dependence structure of some financial time series. The key points and main achievements of this work are listed as follows:1. A new methodology is proposed based on the conditional probability of Markov chains of order 1 and copula theory to identify the dependence between time series of equity returns. A model for the temporal and contemporaneous dependence of vector time series is established to investigate the dependence between them by combining these two theories.In this paper, we propose a parametric estimation model that uses a three-stage pseudo maximum likelihood estimation (3SPMLE). The method of parametric estimation is helpful to the issue "dimension averseness".Based on the 3SPMLE, the properties of parametric estimation, the consistency and asymptotic normality, are studied, and approximate calculations of asymptotic normal variance matrixes are given. The proposed model combines the concept of a copula and the methods of parametric estimators of two-stage pseudo maximum likelihood estimation (2SPMLE). The selection of a copula model that best captures the dependence structure is a critical problem. To solve this problem, we propose a model selection method that is based on the parametric pseudo-likelihood ratio (PPLR) under the 3SPMLE for stationary Markov vector-type models.The method of simulation to the model is proposed. Furthermore, a Monte-Carlo simulation is employed to examine the performance of 3SPMLE of model.Furthermore, we apply the model to study the dependence of equity returns obtained from three major stock markets. The dependence structure will perform well if it takes the temporal dependence of marginal variables into consideration.2. Based on the VAR error correction model and associated with copula technique, a VAR-Copula model is structured to research the Granger causality relation and the dependence structure between the stock price and the trading volume. The empirical study to three stock markets finds that there is a long-rang co-integration between stock price index and the trading volume and a unilateral Granger causality relationship from stock price to the trading volume, and also finds that the complex dependence relationship between the stock price index logarithmic difference and the trading volume logarithmic difference is positive dependence as well as negative dependence and the asymmetrical dependence structure with higher upper tail to all stock markets.An ARMA-GARCH-Copula model is proposed to investigate the contemporaneous dependence relationship between the trade-volume and the stock price and to examine the effect of trading volume on GARCH effect of conditional volatility of stock price about the different data of Shanghai and Shenzhen stock markets price indices and the trading volumes. Moreover, the standard residual data ofthe model is employed to research the dependence structure between Shanghai and Shenzhen stock markets. The results show that the contemporaneous dependence between the return(volatility)-volume logarithm and the daily stock price indices is stronger than that between the volume logarithm and the daily stock price indices. The GARCH effect of the conditional volatility of stock price indices which is explained by trading volume is weak. There is very strong positive dependence relationship between Shanghai and Shenzhen stock markets about the extreme differences of stock price indices and the returns of stock price indices, and an asymmetrical dependence structure of the upper tail higher than the lower tail.3. Based on the higher moment risks of assets and copula, a Copula-NAGARCHSK-M model is established to study the dependence relationships between two time series, and extended to multivariate model from the bivariate.Integrating the time-varying and the asymmetry of higher moment of univariate time series volatility and copula theory, a dependence structure model, Copula-TARCHSK-M model, is proposed to study the dependence structure between time series, and extended to multivariate model from the bivariate in this paper.In addition, the copula functions are firstly employed to study the entropy theory and a conception of dependence structure entropy is defined for measuring the dependence structure of random variables. The joint entropy is separated into the dependence structure entropy and the marginal entropy which is useful of investigating the dependence structure of random variables. Moreover, we also discuss the invariability of dependence structure entropy of bivariate variables under monotonous transforming and extend it to multivariable cases.