Correlation Analysis Of Security Markets Based On Copula Functions

With the development of financial markets,analyzing of single market can not meet the needs of financial research,and describing the dependence structure of the security markets comprehensively and accurately is being the key to financial risk management.The traditional linear correlation coefficient can only measure linear correlation.But financial time series tend to have fat tails,and they does not always have variance,so the linear correlation coefficient can not be used to reflect their relevance.Usually,Granger causality test can conclude qualitative results only and can not make quantitative conclusions.As more flexible and robust nonlinear correlation measurement tools,copula functions have been widely used in financial modeling. Based on the copula functions,the thesis builds a Copula-GARCH(1,1)-t model to measure the correlation degree of Shanghai and Shenzhen security markets and the tail dependence structure of them.The main achievements of this thesis are as follows:Firstly,it reviews the main research achievements of copula functions in financial field.It gives an introduction to the research situation of correlation analysis in financial field by copula functions at home an abroad in detail after defining the concept of correlation.Secondly,it gives the definitions,classifications,characteristics,distribution functi- -ons and density functions of different families of copula functions.It gives an introduction to a variety of relevance indicators entirely,and it gives the definiton of relevance indicators of copula functions.Thirdly,it proposes the construction ideas of financial model on the basis of copula functions and gives an introduction to the main marginal distribution models (includes ARCH models and SV models) of financial time series.Fourth,it estimates the parameters of Copula-GARCH(1,1)-t model built on the Shanghai 180 Index and the Shenzhen Component Index's daily return to study the correlation structure between the two security markets;and it makes comparative study of the tail correlation between the two indexes in two typical periods to observe the different characteristics of different copula functions'ability to capture the stock markets'ups and downs.Firstly,it uses GARCH(1,1)-t Model to fit the marginal distribution of these two indexes.Secondly,it yields two joint distribution functions on the basis of Gumbel Copula and Clayton Copula which belonges to the Archimedean family of copula functions to reflect the actual distribution and relevance of the two indexes'return respectively.It estimates copulas'parameters by the method of Genest and Rivest to explain the structure feature of the tail dependence between the returns of the two markets empirically.The results show that the relevance between Shanghai and Shenzhen stock markets is positive and the correlation degree of lower tail dependence is greater than that of upper tail dependence.Also,it makes comparative analysis of the tail dependence between typical periods of the Shanghai and Shenzhen stock indexes to explore that Clayton Copula function has more significant ability to capture the lower tail dependence.Not only in the down period,but also in the rise consolidation phase of the stock markets,Clayton Copula can capture the correlation between the negative rates of return yielded by the fluctuations of stock prices sensitively.The ability of Gumbel Copula to capture the upper tail dependence remains to be further verified.Fifth,it summarizes the main ideas of the thesis and the application prospect of copula functions.The main innovations of the thesis are as follows:â‘ Breaking through the constraints of the traditional linear correlation,it revises the financial model which combines the newly emerging technology copula functions with the marginal distribution models of financial time series and uses the model to analyze the nonlinear correlation structure of Shanghai and Shenzhen stock markets.The empirical results show that the model fits the financial time series data appropriately and reflects the strong correlation between the two security markets and the asymmetric tail dependence of them correctly.â‘¡Comparative study is made to judge the ability of different copulas to capture the correlation structure of financial time series under different market conditions(the two typically soaring and plunged periods).Up to now,not much research has been done in this area.