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Statistical properties of absolute log-returns and a stochastic model of stock markets with heterogeneous agents

  • Taisei Kaizoji

This paper is intended as an investigation of the statistical properties of {\it 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.\par To further explore these empirical findings, we have introduced a model of stock markets which was proposed in [19,20]. In this model, the stock market is composed of two groups of traders: {\it the fundamentalists}, who believe that the asset price will return to the fundamental price, and {\it 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 is generated by the interacting traders' herd behavior, and, inversely, when the number of fundamentalists is greater than the number of interacting traders, the exponential distribution of absolute log-returns is generated.

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File URL: http://arxiv.org/pdf/physics/0603139
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Paper provided by arXiv.org in its series Papers with number physics/0603139.

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Date of creation: Mar 2006
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Publication status: Published in in T. Lux, S. Reitz, and E. Samanidou (eds.): Nonlinear Dynamics and Heterogeneous Intercting Agents: (Lecture Notes in Economics and Mathematical Systems 550), pp. 237-248, Springer-Verlag, Berlin- Heidelberg (2005)
Handle: RePEc:arx:papers:physics/0603139
Contact details of provider: Web page: http://arxiv.org/

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