Studies Of Chinese Capital Market Based On Fractal Market Theory And Copula Theory

In this dissertation, Fractal Market Theory and Copula theory are introduced.Based on them, Copula-FITSGARCH model is proposed. Then theCopula-FITSGARCH model is demonstrated in Chinese capital market. The mainwork and achievements of this dissertation are listed as follows:1. Fractal Market Theory is studied thoroughly, and it offers the theoryfoundation for the research of this dissertation. Firstly, the Efficient Market Theory isintroduced, and its limitations and the cause of the limitation are pointed out. Then,the fractal theory and its mechanism are introduced. And then, the Fractal MarketTheory is researched and the inherent mechanism, basic behaviors, and economicmeanings of fractal markets are analyzed. At last, the mathematical models that canexhibit the fractal characteristic are researched, and it offers the mathematicalmodeling foundation for the research of this dissertation. Firstly, the fractiondimension time series models include FBM, FDN, I(d), ARFIMA Model, FIGARCHModel and FITSGARCH model.2. The Hurst index which can display the fractal characteristic is introduced.Then, the R/S approach and the modified R/S approach, which are used to discern theHurst index, are introduced. Following that is the V statistic. At last, Chinese CapitalMarket is researched using the R/S and the modified R/S approach, and the fractalcharacteristic of Chinese Capital Market is discerned.3. Copula theory is introduced, and it offers the approach foundation for theresearch of this dissertation. Firstly, the definition, the fundamental characteristic andrelated theorems of Copula theory are introduced. Then, the measures of dependenceand consistency based on Copula are investigated. At last, the popular Copulafunctions are introduced, which include multiple dimensions normal Copula, multipledimensions t-Copula, Archimedes Copula, Extremum Copula and so on.4. On the basis of the theory foundation, the approach foundation and themathematical modeling foundation, the Copula-FITSGARCH model is constructed,which can not only exhibit the fractal characteristic of capital market, but also exhibitthe nonlinear dependence of variables. Then, we use the estimation way of two-stepmaximum likelihood and the Tabu Search Genetic Algorithms to estimate thecoefficients of the Copula-FITSGARCH model, and test the model with K-S testingmethod and χ 2testing method. At last, we use the model to study Chinese capitalmarket and we conclude that the Copula-FITSGARCH model is valid in Chinesecapital market.5. We apply the Copula-FITSGARCH model to identify portfolio VaR. At first,the traditional approaches used to measure risk are introduced. Then the VaR theory,the principle of VaR and the approach to compute VaR are introduced. Then we studyhow to deal with the portfolio VaR with Copula model and multiple-dimensionconditional normal model. And then we compute the portfolio VaR of Chinese capitalmarket using Copula-FITSGARCH model and two-dimension conditional normalmodel respectively. By the back-testing method, we can see the Copula-FITSGARCHmodel works better than the two dimension conditional normal model.