Endogenous versus exogenous origins of financial rallies and crashes in an agent-based model with Bayesian learning and imitation

We present a simple agent-based model to study how the proximate triggering factor of a crash or a rally might relate to its fundamental mechanism, and vice versa. Our agents form opinions and invest, based on three sources of information, (i) public information, i.e. news, (ii) information from their “friendship” network, promoting imitation and (iii) private information. Agents use Bayesian learning to adapt their strategy according to the past relevance of the three sources of information. We find that rallies and crashes occur as amplifications of random lucky or unlucky streak of news, due to the feedback of these news on the agents’ strategies into collective transient herding regimes. These ingredients provide a simple mechanism for the excess volatility documented in financial markets. Paradoxically, it is the attempt for investors to learn the level of relevance of the news on the price formation which leads to a dramatic amplification of the price volatility due to their collective search for the “truth”. A positive feedback loop is created by the two dominating mechanisms (Bayesian learning and imitation) which, by reinforcing each other, result in rallies 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 rallies and crashes are qualitatively different from the rest of the price moves.