This thesis aims at providing insight into comovements of financial assets at high frequency from an original point of view. We take advantage of a database of tick-by-tick prices to bring to light new stylized facts on high frequency correlation as well as to check the empirical validity of multivariate modelling frameworks. In chapter 1, we elaborate on the reasons why high frequency correlation is of the utmost importance for trading purposes. We also briefly review the empirical and theoretical literature on correlation at small time scales. Then, we describe the main features of the data set we use. Finally, we enunciate the results obtained in this thesis. In chapter 2, we suggest a way of extending the subordination modelling to the multivariate case. This relies on the definition of a global event time that merges the trading activity of all assets under consideration. We test the ability of our model to capture salient features of the empirical multivariate probability distribution of returns and find a convincing agreement. In chapter 3, we study high frequency lead/lag relationships using a suitable cross-correlation estimator for tick-by-tick data. We show its superiority over the classical correlation estimator in detecting lead/lag patterns. We relate lead/lag to standard liquidity measures and exhibit a trade-off to find optimal pairs for lead/lag trading. Finally, we evaluate the performance of a lead/lag indicator in forecasting the short-term evolution of prices. In chapter 4, we focus on the intraday correlation seasonal pattern. We estimate this pattern over four universes of stocks and observe striking similarities. We attempt to incorporate this stylized fact into a tick-by-tick price model based upon Hawkes processes. The resulting model captures the empirical profile of correlation quite well, though it doesn’t match the absolute level of correlation.
