Pair Copula-GARCH Modeled By Vines And Its Empirical Research

Pair copula decomposition modeled by vines is a new method which appears in the field of copula theory recently. Based on the new graphical model called vine, we use a series of pair copula building blocs to construct multivariate distributions by which we can analyst the dependence among the general multivariate, especially in the higher-dimensional situations. Contrast to describing the multivariate distributions with n dimensional copula function directly, Pair copula model decomposes the multivariate distributions with a cascade of pair copula, acting on two variables at a time and organized by vines. The pair copulas do not have to belong to the same family. Given data and assumed pair copula decomposition, we can choose for each pair of variables the parametric copula that best fits the data. In this way, the resulting multivariate distribution will be valid. Besides, the VaR value of the portfolio based on the Pair copula decomposition is more accurate because it concludes more information about complex patterns of dependence in the tails. This dissertation consists of four chapters.Chapter one is the introduction. We introduce the research background firstly. The current situation of copula theory, copula-GARCH model and Pair copula decomposition is discussed in detail. We also list the past research results in these field. This research problem and significance of this paper is argued from three aspects. At last, we mention the data resource and the analysis software.In Chapter two, we introduce the Copula function, such as its definition, properties, estimation and simulation. Based on the copula theory, we discuss kinds of copula-GARCH models and their constructions. The estimation of these models decomposes into two parts: ARCH model and copula model.In Chapter three, we propose the pair copula-GARCH mode and its estimation which is based on the vine and pair copula model. Combined with Monte Carlo simulation technology and pair copula-GARCH model, we propose the procedure of calculating the portfolio's VaR. At last, we used the data picked up from Shanghai stock market to empirical analyze the maneuverability of this model.Chapter four summarizes the research results and argues the prospects.