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:: Herding Behaviour in Financial Markets ::

We have already had a first hand demonstration of the non-gaussian behaviour of market prices. Why is this so, and why does the Black-Scholes have this weakness? It appears that a key ingredient(s) is missing or miss represented in the model. One needs to firstly identity qualitatively the effect(s), and then, make a quantified description. Primarily, we are concerned with explaining why our probability distribution are leptokurtic?

To do this, one needs to consider the market on a microscopic scale, i.e. the individual investors and their interaction with one another. Furthermore, how do the individuals react to external factors. e.g. political news, the weather, etc.

So far, we have used the EMT to assume no interactions between investors. From a statistical mechanical point of view, the absence of interaction between investors translates into no correlations between difference agents. As human beings have memory and past events influence our decision making. Thus, we need to introduce some interaction factor between the agents (traders).

There are innumerable social and economic situations in which we are influenced in our decision making by what others are doing. A very common example would be bars or restaurants people go to because the are said to be 'popular' or 'trendy'. The same is true for academic researchers who choose to work on a topic that is currently 'hot'. Financial markets are no exceptions to herding effect. Many investors copy cat the actions of other investors who they may regard as having reliable information or knowledge about the market.

Imitation and herding can account for the statistical nature of market dynamics where there are periods of stable prices followed by sudden extreme fluctuations - a property often referred to as intermittency like that seen in fluid dynamics. When investors form groups that copy one another (herds) it can be intuitively seen how this factor, coupled with the law of supply and demand, will cause sudden rises (falls) when they all decide to buy (sell). This will be reflected in the leptokurtosis of the price fluctuation distributions. The groups remain innactive for long periods until one (or some) of its members become actives. If the herding behaviour is large enough, investors will act collective to induce market crashes. Fortunately, not all the market is dominated by herding and many individuals choose to use their own brains in making decisions.

Recently, there have been numerous models put forward to explain the dynamics of asset prices and market crashes, some more realistic than others. These include models with clusters of investors representing separate groups sharing the same information that acting together, and some similar to the Ising model requiring the use of the renormalisation calculations. None of these models can capture and reproduce all the features of market behaviour, suggesting the problem in more complicated.

Written by Alessio Farhadi

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