Volatility and Dependence Models with Applications to U.S. Equity Markets

The dissertation consists of three studies concerning the research fields of evaluating volatility and correlation forecasts as well as modeling of tail dependence. Based on theoretical discussions and empirical studies the methods for modeling the time-varying volatilities and dependence for the financial market data are evaluated. The first study evaluates the volatility forecasts with the basic generalized conditional autoregressive heteroskedasticity (GARCH) model and its asymmetric extensions. The concepts of loss function and model confidence set (MCS) are introduced. The realized volatility is used as benchmark. The main results of Brownlees et al. (2011) can be confirmed and extended. In particular, the one-step forecasts achieve significantly lower average losses than the multi-step forecasts in times of crises. The difference between the one-step and the multi-step forecasts in pre-crisis times is relatively small. The evaluation results demonstrate the strong forecasting performance of the asymmetric model variants. The second study evaluates the multivariate correlation forecasts. The Baba-Engle-Kraft-Kroner (BEKK) model of Engle and Kroner (1995) is compared with the dynamic conditional correlation (DCC) model of Engle (2002). Using a two-stage estimation method, the DCC model is well suited for large correlation matrices. In contrast, the more flexible BEKK model suffers from the curse of dimensionality. The evaluation is based on the class of asymmetric loss functions proposed by Komunjer and Owyang (2012). The results show that the BEKK model cannot better predict the correlations than the simpler DCC model in the trivariate system. Therefore, the application of the DCC model appears to be superior. The third study leads to a flexible approach which separates the univariate marginal distributions from the joint distribution. The different copula functions are presented and the corresponding tail dependence is calculated. The empirical analysis compares different copula functions with a non-parametric approach and three time-dependent approaches. The results show noticeable reactions of tail dependence to the major financial market events. In addition, the lower tail dependence dominates over time. This can be interpreted in a way that joint losses occur more frequently than joint gains.