Modelling and measuring jumps in high frequency data

The paper summarizes the latest developments in volatility modelling with jumps. It undertakes a comprehensive review of the literature written, highlighting the relevance of the topic and the improvements brought by departing from continuous sample path models to nonparametric realized volatility models which account for jumps. Three of the most relevant tests (Sahalia and Jacod, 2012, Barndorff-Nielsen and Shephard, 2006, and Lee and Mykland, 2007) are succinctly described.