  We present a simple agent-based model to study the development of a bubble
and the consequential crash and investigate how their proximate triggering
factor might relate to their fundamental mechanism, and vice versa. Our agents
invest according to their opinion on future price movements, which is based on
three sources of information, (i) public information, i.e. news, (ii)
information from their "friendship" network and (iii) private information. Our
bounded rational agents continuously adapt their trading strategy to the
current market regime by weighting each of these sources of information in
their trading decision according to its recent predicting performance. We find
that bubbles originate from a random lucky streak of positive news, which, due
to a feedback mechanism of these news on the agents' strategies develop into a
transient collective herding regime. After this self-amplified exuberance, the
price has reached an unsustainable high value, being corrected by a crash,
which brings the price even below its fundamental value. These ingredients
provide a simple mechanism for the excess volatility documented in financial
markets. Paradoxically, it is the attempt for investors to adapt to the current
market regime which leads to a dramatic amplification of the price volatility.
A positive feedback loop is created by the two dominating mechanisms
(adaptation and imitation) which, by reinforcing each other, result in bubbles
and crashes. The model offers a simple reconciliation of the two opposite
(herding versus fundamental) proposals for the origin of crashes within a
single framework and justifies the existence of two populations in the
distribution of returns, exemplifying the concept that crashes are
qualitatively different from the rest of the price moves.
