Essays on Models for Financial Volatility

This research is focused on models for volatility. After the introduction of realized volatility as a consistent estimator for daily volatility, time series models without latent variables have been used to model and forecast volatility. The first part of this research provides a critical review of some of the commonly used realized volatility models and addresses the problem of stationarity and lag selection. In the empirical part we apply our methodology to thirty Dow Jones Industrial Average stocks from the NYSE TAQ dataset. We address the lag selection problem for each of the stocks considered. We find that models based on flexible lag structures do not significantly outperform models based on a fixed lag structure.With respect to latent model specifications for volatility, this study analyzes how the correlation structures in ARCH models relate to those in HARCH models. ARCH models have correlation structures that can be interpreted in the sense of mean reversion. HARCH rely on a specification that includes squared aggregated returns in the conditional variance equation. We find that HARCH is not able to capture correlation scales from ARCH in the mean reverting sense. This finding has implications for persistence. The corresponding persistence measure in HARCH does not capture the persistence of ARCH. In order to address these problems an optimal lag structure is identified. The correspondence between the lag structure and serial correlation is also addressed.In the last part of this study a Bayesian framework is employed in order to investigate the post storm firm survival after hurricanes Katrina and Rita in the Orleans Parish, Louisiana. A novelty of this approach is the spatial component in the model specification. Bayesian techniques are employed in order to draw inferences from a spatial probit model on a dataset containing 8,171 firms from the Orleans Parish. We find evidence indicating the presence of spatial components, especially in the quarters immediately following the storms. Other findings are: larger firms are more likely to survive; also, less flooded firms are more likely to survive; finally, sole proprietorships are more likely to reopen than large chain stores.