Three Essays on Estimation and Dynamic Modelling of Multivariate Market Risks using High Frequency Financial Data

This dissertation consists of three stand-alone research papers, all of which treat the topic of estimation and dynamic modelling of multivariate volatility by employing the information contained in high-frequency data, which became available in the last 10 - 15 years. The main focus of all three studies is the multivariate application, in which one is interested in estimating and modelling the covariance matrix of more than two financial assets. Main motivation is that in practice, an economic agent is rarely exposed to a single source of risk, and it is exactly the correlations between risks, which make risk management so important. If risks were not correlated, the concepts of hedging, portfolio diversification and risk management would not have come into existence. The availability of high-frequency data opened new frontiers in the field of risk management not only to financial econometricians and mathematicians, but also to practitioners, who are now able to measure and manage risk much more accurately than only several years ago. It is exactly this relevance and novelty of the field that makes it currently a very active area of research.The three chapters of this thesis can broadly be separated into two categories - estimation (Chapter 1 and 2) and dynamic modelling (Chapter 3), and are intentionally arranged in a particular sequence in the thesis. The first paper is mainly concerned with how to obtain a precise estimate of the covariance between two assets in the presence of a host of market microstructure frictions. An extension to this problem, where both the estimation of variances and covariances is addressed in a theoretically unified framework, is presented in the second paper, which also develops new estimation techniques improving substantially the efficiency of existing univariate and multivariate estimators. In the third chapter I abstract from the issue of market microstructure, starting from the point where a series of covariance matrices is available, for which a suitable time-series model is to be developed with the aim of making risk forecasts. Thus, the exposition in the thesis evolves logically from the problem of estimating a single covariance, through the estimation of a possibly high-dimensional covariance matrix, to the issue of dynamic modelling and forecasting of the multivariate risks.