Analysis of multivariate volatiliaty

It is famous, that majority of assets correlates with each other and we can demonstrate it easily. We can see dependence between assets on different markets. That’s why it is stupid to ignore this correlation. But the majority of risks metrics was built on statistics of only one asset. The results of such modeling were not high. In order to solve this problems, researchers paid attention to multivariate models. The main target of this work is to learn possibilities of multivariate returns of financial assets modeling. The work pays special attention to multivariate volatility models.In the first part of work, we expand univariate models on multivariate situation. Thus, we can use Vector Avtoregression as multivariate situation of AR process. The examples of multivariate volatility models are BEKK, EWMA, CCC-MGARCH, DCC-MGARCH and so on. Besides, we pay attention to copula functions what is good possibility to analyze specific structure of correlation. Copula function can dramatically increase estimation efficiency of multivariate models. In the second part of work, we learn practical aspects of multivariate volatility models. First of all, we pay our attention to models with dynamic correlation matrix (there is situation when correlation matrix depends on its past values). This is key difference between constant correlation matrix models (such as CCC-MGARCH) and dynamic correlation matrix model (such as DCC-MGARCH and Copula-MGARCH). We compare estimation efficiency of DCC-MGARCH and Copula-MGARCH on example of MMVB and S&P500 index. The coefficient estimations are similar, but information criteria of Copula-MGARCH is better. Besides, we demonstrate methodology of Copula-MGARCH models for Value at Risk estimations. Object of this research is multivariate models of financial returns. The subject of this work is statistical data, articles and so on. We use statistical software R-project.