Multivariate volatility models and their applications

Cross-variable interactions are key in macroeconomics and finance. It is now widely accepted that financial volatilities move together over time across assets and markets. Recognizing this feature through a multivariate modelling framework leads to more relevant empirical models than working with separate univariate models. From a financial economics point of view, it opens the doors to better decision tools in various areas such as asset pricing models, portfolio selection and risk management. In the recent literature we see a great development in the econometric specifications of multivariate models, in particular GARCH-type models. But comprehensive evaluations of the empirical importance of these models (especially, recent ones) and of the optimal ratio between flexibility and parsimony of model specifications are still an open question. Because of computational complexity, preference in the applied literature is given to parsimonious specifications with little cross-variable volatility interaction. Therefore, we address the question whether restrictions imposed by parsimonious model specifications play an important role in the empirical applications. Moreover, since all models in the literature can be seen as natural extensions of popular univariate GARCH models it remains an open issue what the consequences of more general models are. The purpose of the project is twofold: 1. We are going to evaluate different multivariate GARCH models to get insights which specifications fit the data best in different financial economics applications. We plan to include in the analysis both the parsimonious models used in the literature and more recent flexible specifications. We will consider the empirical evaluation of these models in the economic context. In particular, we will apply the models to such important fields as asset pricing, volatility transmission, portfolio construction and Value-at-Risk calculations. 2. Within more exploratory work, we would like to extend our experience with neural network based non-linear volatility modeling to the multivariate case and test the degree of non-linearity in different financial data within the multivariate framework.

Cross-variable interactions are key in macroeconomics and finance. It is now widely accepted that financial volatilities move together over time across assets and markets. Recognizing this feature through a multivariate modelling framework leads to more relevant empirical models than working with separate univariate models. From a financial economics point of view, it opens the doors to better decision tools in various areas such as asset pricing models, portfolio selection and risk management. In the recent literature we see a great development in the econometric specifications of multivariate models, in particular GARCH-type models. But comprehensive evaluations of the empirical importance of these models (especially, recent ones) and of the optimal ratio between flexibility and parsimony of model specifications are still an open question. Because of computational complexity, preference in the applied literature is given to parsimonious specifications with little cross-variable volatility interaction. Therefore, we address the question whether restrictions imposed by parsimonious model specifications play an important role in the empirical applications. Moreover, since all models in the literature can be seen as natural extensions of popular univariate GARCH models it remains an open issue what the consequences of more general models are. The purpose of the project is twofold: 1. We are going to evaluate different multivariate GARCH models to get insights which specifications fit the data best in different financial economics applications. We plan to include in the analysis both the parsimonious models used in the literature and more recent flexible specifications. We will consider the empirical evaluation of these models in the economic context. In particular, we will apply the models to such important fields as asset pricing, volatility transmission, portfolio construction and Value-at-Risk calculations. 2. Within more exploratory work, we would like to extend our experience with neural network based non-linear volatility modeling to the multivariate case and test the degree of non-linearity in different financial data within the multivariate framework.