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Mixed Copula Construction And Applications

Posted on:2011-12-28Degree:MasterType:Thesis
Country:ChinaCandidate:Y MaFull Text:PDF
GTID:2199330332972967Subject:Applied Mathematics
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Dependence relations between random variables is one of the most widely studied subjects in Probability and statistics. But the traditional correlation coefficients have some limits for a measure of the dependence between random variables. Using copula for measuring dependence takes more attentions in recent years.The term Copula is based on the notion of "coupling", the Copula couples the marginal distributions together to form a joint distribution. The dependence relationship is entirely determined by the Copula, while statistical descriptions are entirely determined by the marginal. Copulas have become a popular multivariate modeling tool in many fields where the multivariate dependence is of great interest and the usual multivariate normality is in question. Conventional methods like correlation summarize dependence, whereas a Copula gives a model for the dependence structure that reflects more detailed knowledge of the random variables. Copulas have become a popular multivariate modeling tool in many fields. If we want to gain the good property of those copula, we could construct the mix copula. And these distributions are always very useful for simulation. Because this, it is meaningful of constructing copula.In this dissertation, The mix copula theory and its applications in multivariate financial time series analysis are studied intensively. One empirical researches of Copula theory in China stock markets are present, it is the dependence research of Index of Shanghai Stock Exchange and Shenzhen.1. Copula theory is summarized systemically and wholly in this dissertation. We present an overview of introduction of Copula, such as the definition and it's main mathematical and modeling properties and the classification. summing up the copula of using in the finance.2. This Paper gives a new method of constructing mix copula depends on the Clayton Copula,Frank Copula and FGM Copula. The Copula is a tool for understanding relationships among multivariate random variable. The research indicates that the two indexes arc strongly positively correlative and the correlation can be characterized by unsymmetrical tail dependence...
Keywords/Search Tags:Copula, dependence, Clayton Copula, Frank Copula, FGM Copula
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