Essays on realized measures of volatility

This thesis investigates the stylized facts of realized measures of volatility in 10 different market sectors. Traditionally, studies in the area have addressed the issues by either using a single measure on a number of stocks or indices, or a number of measures on a given stock or an index. This usually provides results that cannot be generalized; hence does not allow for discussing these measures comparatively, nor fully quantifies the gains from using high frequency data in general. Using 100 stocks from 10 sectors over the period 2000 - 2010, we investigate topics within the high frequency context of various realized volatility measures. In Chapter 1, we investigate whether the stylized facts of different realized measures vary across sectors. To this end, our work could be seen as an extension of Andersen et al (2001), Luu and Martens (2003), Andersen et al (2010), Fleming and Paye (2011), and Giot et al (2010). Our findings here are of interest as it provides guidance as whether certain realized measures are best suited to address specific queries relative to others. In Chapter 2, we revisit the volatility-volume (number of trades) relation. The literature takes it as a task to establish as which is a better measure of the market activity. Despite numerous studies, this remains an open question, a query that we will address as a part of our investigation. We revisit this relation within the context of what is known as the mixture of distributions hypothesis. We aim to investigate whether this relation is stable across different sectors and whether it is measure dependent. We also aim to show that the information content between the two activity measures is distinct. We find that on average, the number of trades is a better proxy for market activity. We also show that a trade that accompanies a price change is more important than one which takes place at the same price. In Chapter 3, we address the issue of recovering returns normality using parametric and non-parametric measures of volatility. Returns are not normal, as evident from the vast number of empirical studies that investigate their stylized facts. The finding that returns normality could be achieved through standardization is based on the assumption that any semi-martingale process could be written as a time-changed Brownian motion. The aim in this chapter is to highlight the important factors that may affect recovering returns normality. We look at factors such as the frequency at which the realized measures are estimated, the level of stock activity, the effect of jumps and micro structure noise. We find that the most dominant factors are the sampling frequency and microstructure noise. Overall, this thesis seeks to investigate the outlined topics to check whether the extensively reported findings still hold by using a very refined data.