Are asset return tail estimations related to volatility long-range correlations?

We discuss a possible scenario explaining in what respect the observed fat tails of asset returns or volatility fluctuations can be related to volatility long-range correlations. Our approach is based on recently introduced multifractal models for asset returns that account for the volatility correlations through a multiplicative random cascade. Within the framework of these models, it can be shown that the sample size required for a correct estimation of the behavior of extreme return fluctuations is generally huge and outside the range of accessible size of data. Consequently, in many cases, the extreme tail probability appears as a power-law, with a rather small (underestimated) tail exponent. We point out that increasing the amount of data by using smaller and smaller (intraday) scales, does not contribute to reduce the bias and, as observed empirically, the tail exponent turns out to be rather stable across scales.