Essays in Modeling of Daily Returns and Realized Volatility

The dissertation presents three essays in the joint modeling of returns and realized volatility. The common characteristic of the three essays is the use of measurements of realized volatility, computed with high frequency data, to improve the fit and forecast of volatility models for daily returns. The relatively easy access to high frequency data makes this approach interesting as intraday data carry much more information about the dynamics of short term variance than low frequency (daily) data does.;The first essay introduces a new multivariate conditional volatility model for returns that utilizes realized covariance matrices. The model decomposes the conditional and realized covariance matrices into standard deviation and correlation matrices. On a first level, the univariate variances are estimated by a modified Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model that exploits intraday information. On the second level the conditional correlation matrices follow a regime switching Markov process. The inference about the regimes and the regime-switching correlations exploits the information contained in the realized correlation. An empirical application shows the ease of estimation and a forecasting exercise shows superior predictive ability when high-frequency information is incorporated.;The second essay puts forward a multivariate extension of a modified GARCH model that incorporates realized measure of covariance. The modification of the multivariate GARCH consists in replacing the outer product of past returns by the past realized covariance matrix. The curse of dimensionality is alleviated by a decentralization of the estimation procedure. The estimation process is computationally easier because there is no need to invert large covariance matrices and can therefore be applied to large data set.;The previous two chapters establish the gain in statistical accuracy of including intraday information in the modeling and forecasting of conditional covariance. The last essay presents empirical evidence on the economic gain to an investor in a situation of portfolio allocation. An empirical exercise presents the economic value of the access to intraday information for an agent who faces a simple asset allocation problem.;As an introduction to the dissertation, chapter one presents the methods used throughout the dissertation to calculate the realized covariance matrices and to compare the different predictions made by the models proposed.