The idea that non-linear dynamics and statistical physics may help unravel the dynamics of stock markets has attracted a good number of researchers (see press release here). The enthusiasm follows empirical evidence that the logarithm price changes may have a scale free or fat distribution tails regime, such as the one found in stock market returns and monetary exchange markets. These findings contrasts the often assumption that price fluctuations follow a log-normal distribution (assumed in the traditional model of options pricing), and are more in accordance to the observation that market crashes occur from time to time. Scale free distributions often arise in statistical physics as systems composed of a large number of ``particles'' is at the verge of a phase transition. This has been the key factor to catalyse a lot of research bringing together the methods and ideas of statistical physics in the realm of financial market modelling.
One of the ideas put forward to explain the fat distribution tails in the price returns of assets, is that of herd behavior [Bannerjee93]. This phenomena corresponds to the fact that many agents in a financial market may act similarly due to the sharing of the same information. This herding, will provoke a large effect in the price of the asset, and this may cause for large fluctuations.
Cont and Bouchaud proposed a bond percolation model to illustrate these ideas. This model assumes that the cluster formation process is independent of the price formation, thus the model requires to adjust a priori a parameter governing the density of links between agents. Each link was to represent a contact, such that when one agent buys or sells a stock, all the corresponding cluster (connected component) will act similarly. We develop a dynamic model where rumors are introduced into the system, and they can serve to either grow the network of connections (the rumor disperses) or destroy a cluster, whenever a whole cluster buys or sells randomly and would also signal the expiration of the rumor.
This simple economics of rumors predicts fat tails with an exponent compatible with some of the empirical observations.
References
In the News Media... (see complete list here)
