Mean Field Effects and Interaction Cycles in Financial Markets

In this work, we investigated the effects of herding on assets price dynamics during the intra-day trading. The model — built as a mean-field in a binary setting (buy/sell decisions) — shows that when the interaction among individuals is low — i.e. there is few herding — the dynamics converges monotonically or with oscillations to the prior about the fundamental value of the asset (assumed constant and homogeneous across individuals). If agents give a larger weight to the action of the others fluctuations are amplified, until a Hopf bifurcation eventually occurs and limit cycles emerge. Simulations with gaussian noise on prices reproduce the same dynamics: rising either the strength of interaction or the intensity of choice the imitative behavior prevails on all other factors, and we have upward and downward rushes. For a wide range of “intermediate” values of parameters, some other interesting features emerge, such as excess kurtosis and clustering in the volatility of returns.