A Binary Decision Model and Fat Tails in Financial Market

Abstract

Binary decision models have been the subject of renewed research in recent years. In these models, agents follow a stochastic evolution where they must choose between two possible choices by taking into account the choices of their peers. Kirman explained the process of ant social herding using a simple model, and he conducted an interesting simulation. The fat-tail distribution in the security market is well known, but its causes have not been sufficiently clarified. The aim of this article is to clarify them by a very simple model. In this article, by establishing a simple security market model and by applying the model of Kirman, the fat tail observed for price fluctuations is reproduced. Recent research in neuroscience has shown that noise plays a positive roll and enables us to have a deeper understanding of a natural commonality between ants and traders. The beauty competition of Keynes is kept in mind, and it is shown that a cause of the fat tail is the balance between independence and interdependence of the economic agents. Using a natural computing algorithm called Kirman’s ant model, I conducted a time series analysis of finance that appears when simplifying the human “behavior of imitating others”. The results show that natural fat tails appear.