Statistical Properties of Absolute Log-Returns and a Stochastic Model of Stock Markets with Heterogeneous Agents

Summary

This paper investigates the statistical properties of absolute log-returns, defined as the absolute value of the logarithmic price change, for the Nikkei 225 index in the 28-year period from January 4, 1975 to December 30, 2002. We divided the time series of the Nikkei 225 index into two periods, an inflationary period and a deflationary period. We have previously [18] found that the distribution of absolute log-returns can be approximated by the power-law distribution in the inflationary period, while the distribution of absolute log-returns is well described by the exponential distribution in the deflationary period.

To explain these empirical findings, we have introduced a model of stock market dynamics [19,20]. In this model, the stock market is composed of two groups of traders: the fundamentalists, who believe that the asset price will return to the fundamental price, and the interacting traders, who can be noise traders. We show through numerical simulation of the model that when the number of interacting traders is greater than the number of fundamentalists, the power-law distribution of absolute log-returns emerges from the interacting traders' herd behavior, and, vice-versa, when the number of fundamentalists is greater than the number of interacting traders, absolute log-returns are characterised by an exponential distribution.