Some properties of the correlation between high frequency financial assets.

Summary The aim of this thesis is to deepen the academic knowledge on the joint variations of high-frequency financial assets by analyzing them from a novel perspective. We take advantage of a tick-by-tick price database to highlight new stylistic facts about high-frequency correlation, and also to test the empirical validity of multivariate models. In Chapter 1, we discuss why high-frequency correlation is of paramount importance to trading. Furthermore, we review the empirical and theoretical literature on correlation at small time scales. Then we describe the main characteristics of the dataset we use. Finally, we state the results obtained in this thesis. In chapter 2, we propose an extension of the subordination model to the multivariate case. It is based on the definition of a global event time that aggregates the financial activity of all the assets considered. We test the ability of our model to capture notable properties of the empirical multivariate distribution of returns and observe convincing similarities. In Chapter 3, we study high-frequency lead/lag relationships using a correlation function estimator fit to tick-by-tick data. We illustrate its superiority over the standard correlation estimator in detecting the lead/lag phenomenon. We draw a parallel between lead/lag and classical liquidity measures and reveal an arbitrage to determine the optimal pairs for lead/lag trading. Finally, we evaluate the performance of a lead/lag based indicator to forecast short-term price movements. In Chapter 4, we focus on the seasonal profile of intraday correlation. We estimate this profile over four stock universes and observe striking similarities. We attempt to incorporate this stylized fact into a tick-by-tick price model based on Hawkes processes. The model thus constructed captures the empirical correlation profile quite well, despite its difficulty to reach the absolute correlation level.