Scaling, stability and distribution of the high-frequency returns of the Ibex35 index

► We analyze high-frequency log-returns of the Ibex35 index in a two year period. ► Maximum likelihood estimation and goodness-of-fit tests for a family of distributions. ► Best fit is given by the NIG distribution, better than Lévy-stable laws. ► Empirical data distribution is stable over several time scales, from seconds to hours. ► Time correlations in the data are necessary to explain the observed stability.