Financial volatility is the core of multiple sectors in finance. This work investigates different aspects of volatility using high-frequency data. High-frequency data offer a complete picture of the dynamics of the intraday patterns, contributing to a more precise
inference about these patterns. However, their complex structural form yields several challenges in the analysis for the practitioners. Our research takes place in both the univariate and multivariate space, meaning that we explore the data characteristics for
every asset separately and as a factor of interactions among the assets.

In terms of the analysis in the univariate space, Chapters 2 and 4 develop some volatility estimators in discrete and continuous time scales, respectively. More specifically, we develop several estimators of the intraday volatility in Chapter 2 where each
estimator approximates the intraday volatility, exploiting different characteristics of the dataset. On the other hand, we consider an estimator of the daily volatility along with its theoretical framework in Chapter 4. Our simulation study shows that our estimator is superior to standard estimators of daily volatility when the variance of the noise incorporated in the intraday observations takes values of normal size.

In the multivariate space, Chapter 3 studies whether we can decompose the daily volatility traits to some components, inferring the assets which drive these components the most. Also, we extend the relevant methodology to volatility estimates with high
frequency, as those provided by the estimators in Chapter 2. Through our proposed approach, we can deduce the stocks which present the highest variability as well as the intraday periods this variability is observed more intensely.

In Chapter 5, we develop a technique for estimating the conditional dependence structure between the assets using the concept of graphical models. This chapter treats high-frequency data as functional data, allowing us to exploit their virtues to draw
inferences about the assets’ conditional interdependencies.