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