We establish several new stylized facts concerning the intra-day seasonalities of stock dynamics. Beyond the well-known U-shaped pattern of the volatility, we find that the average correlation between stocks increases throughout the day, leading to a smaller relative dispersion between stocks....

We revisit the index leverage effect, that can be decomposed into a volatility effect and a correlation effect. We investigate the latter using a matrix regression analysis, that we call ‘Principal Regression Analysis’ (PRA) and for which we provide some analytical (using Random Matrix...

We propose a general framework to study the stability of the subspace spanned by P consecutive eigenvectors of a generic symmetric matrix H0 when a small perturbation is added. This problem is relevant in various contexts, including quantum dissipation (H0 is then the Hamiltonian) and financial...