  We introduce a minimal Agent Based Model with two classes of agents,
fundamentalists (stabilizing) and chartists (destabilizing) and we focus on the
essential features which can generate the stylized facts. This leads to a
detailed understanding of the origin of fat tails and volatility clustering and
we propose a mechanism for the self-organization of the market dynamics in the
quasi-critical state. The stylized facts are shown to correspond to finite size
effects which, however, can be active at different time scales. This implies
that universality cannot be expected in describing these properties in terms of
effective critical exponents. The introduction of a threshold in the agents'
action (small price fluctuations lead to no-action) triggers the
self-organization towards the quasi-critical state. Non-stationarity in the
number of active agents and in their action plays a fundamental role. The model
can be easily generalized to more realistic variants in a systematic way.
