  Using high frequency data, we have studied empirically the change of
volatility, also called volatility derivative, for various time horizons. In
particular, the correlation between the volatility derivative and the
volatility realized in the next time period is a measure of the response
function of the market participants. This correlation shows explicitly the
heterogeneous structure of the market according to the characteristic time
horizons of the differents agents. It reveals a volatility cascade from long to
short time horizons, with a structure different from the one observed in
turbulence. Moreover, we have developed a new ARCH-type model which
incorporates the different groups of agents, with their characteristic memory.
This model reproduces well the empirical response function, and allows us to
quantify the importance of each group.
