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Statistical properties of absolute log-returns and a stochastic model of stock markets with.pdf

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

a r X i v : p h y s i c s / 0 6 0 3 1 3 9 v 1 [ p h y s i c s .s o c - p h ] 1 7 M a r 2 0 0 6 Statistical properties of absolute log-returns and a stochastic model of stock markets with heterogeneous agents Taisei Kaizoji 1. Division of Social Sciences, International Christian University 3-10-2 Osawa, Mitaka, Tokyo 181-8585, Japan. 2. Econophysics Laboratory, 5-9-7-B Higashi-cho, Koganei-shi, Tokyo 184-0011, Japan. kaizoji@icu.ac.jp, http://subsite.icu.ac.jp/people/kaizoji/ Summary. This paper is intended as an investigation of 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 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 com- posed 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 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. Key words: absolute log-returns; exponential laws; power laws; infla- tion; deflation; a stochasti