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We investigate the volatility return intervals in the NYSE and FOREX markets.We explain previous empirical findings using a model based on the interactingagent hypothesis instead of the widely-used efficient market hypothesis. Wederive macroscopic equations based on the microscopic herding interactions ofagents and find that they are able to reproduce various stylized facts ofdifferent markets and different assets with the same set of model parameters.We show that the power-law properties and the scaling of return intervals andother financial variables have a similar origin and could be a result of ageneral class of non-linear stochastic differential equations derived from amaster equation of an agent system that is coupled by herding interactions.Specifically, we find that this approach enables us to recover the volatilityreturn interval statistics as well as volatility probability and spectraldensities for the NYSE and FOREX markets, for different assets, and fordifferent time-scales. We find also that the historical S\&P500 monthly seriesexhibits the same volatility return interval properties recovered by ourproposed model. Our statistical results suggest that human herding is so strongthat it persists even when other evolving fluctuations perturbate the financialsystem.

Stochastic model of financial markets reproducing scaling and memory in volatility return intervals