Stock index dynamics worldwide: a comparative analysis

We perform a comparative analysis of twenty-four daily stock indices across the world, encompassing developed and emerging markets. We compute, directly from the return empirical time series, the Kramers-Moyal (KM) expansion coefficients that govern the evolution of the probability density function of returns throughout timelags. Our study discloses universal patterns of the KM coefficients, which can be described in terms of a few microscopic parameters. These parameters allow to quantify features such as deviations from Gaussianity or from efficiency, providing a tool to discriminate market dynamics.