The goal of this paper is twofold. First, using five of the most actively traded stocks in the Brazilian financial market, this paper shows that the normality assumption commonly used in the risk management area to describe the distributions of returns standardized by volatilities is not compatible with volatilities estimated by EWMA or GARCH models. In sharp contrast, when the information contained in high frequency data is used to construct the realized volatility measures, we attain the normality of the standardized returns, giving promise of improvements in Value-at-Risk statistics. We also describe the distributions of volatilities of the Brazilian stocks, showing that they are nearly lognormal. Second, we estimate a simple model of the log of realized volatilities that differs from the ones in other studies. The main difference is that we do not find evidence of long memory. The estimated model is compared with commonly used alternatives in out-of-sample forecasting experiment.

Publicado na Revista Brasileira de Finanças, Volume 4, p.321-343, 2006

This article reviews the exciting and rapidly expanding literature on realized volatility. After presenting a general univariate framework for estimating realized volatilities, a simple discrete time model is presented in order to motivate the main results. A continuous time specification provides the theoretical foundation for the main results in this literature. Cases with and without microstructure noise are considered, and it is shown how microstructure noise can cause severe problems in terms of consistent estimation of the daily realized volatility. Independent and dependent noise processes are examined. The most important methods for providing consistent estimators are presented, and a critical exposition of different techniques is given. The finite sample properties are discussed in comparison with their asymptotic properties. A multivariate model is presented to discuss estimation of the realized covariances. Various issues relating to modelling and forecasting realized volatilities are considered. The main empirical findings using univariate and multivariate methods are summarized.

Publicado na Econometric Reviews, v. 27, jan-junho 2008

Does volatility reflect a continuous reaction to past shocks or do changes in the markets induce shifts in the volatility dynamics? In this paper, we provide empirical evidence that cumulated price variations convey meaningful information about multiple regimes in the realized volatility of stocks, where large falls (rises) in prices are linked to persistent regimes of high (low) variance in stock returns. Incorporating past cumulated daily returns as an explanatory variable in a flexible and systematic nonlinear framework, we estimate that falls of different magnitudes over less than two months are associated with volatility levels 20% and 60% higher than the average of periods with stable or rising prices. We show that this effect accounts for large empirical values of long memory parameter estimates. Finally, we show that, while introducing more realistic dynamics for volatility, the model is able to overall improve or at least retain out-of-sample performance in forecasting when compared to standard methods. Most importantly, the model is more robust to periods of financial crises, when it attains significantly better forecasts.

Publicado em International Journal of Forecasting, v.25, p. 304-327, 2009

publicado na Pesquisa e Planejamento Econômico, v. 36, n. 3, 2006

publicado em Journal of Political Economy, v. 116, n.61, p. 1058-1104, 2008

publicado em Population and Development Review, v. 33, n.2, p.247-287,  junho 2007