Abstract: The multiscale self-similarity and hierarchy properties of asset volatility are investigated by structure functions and hierarchical models.The available empirical results show that volatility manifests self-similarity only for certain scales and amplitudes measured by the ordinary and relative structure funcdons.While the normalized relative structure function with more universality is further utilized, volatility exhibits the significant self-similarity at the whole scales.In addition, the significant power relations based on the new normalized hierarchical model, contrary to the scatteredphenomena of SL model, conclude that the volatilities imply the ‘neighboring' hierarchy different from the highest stimulated states(the strongest intermittent structures) of SL hierarchy.

Key words: multiscale, structure function, self-similarity, hierarchy