dorsal/arxiv
View SchemaStatistical properties of absolute log-returns and a stochastic model of stock markets with heterogeneous agents
| Authors | Taisei Kaizoji |
|---|---|
| Categories | |
| ArXiv ID | physics/0603139 |
| URL | https://arxiv.org/abs/physics/0603139 |
| DOI | 10.1007/3-540-27296-8_16 |
| Journal | 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) |
Abstract
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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"abstract": "This paper is intended as an investigation of the statistical properties of\n{\\it absolute log-returns}, defined as the absolute value of the logarithmic\nprice change, for the Nikkei 225 index in the 28-year period from January 4,\n1975 to December 30, 2002. We divided the time series of the Nikkei 225 index\ninto two periods, an inflationary period and a deflationary period. We have\npreviously [18] found that the distribution of absolute log-returns can be\napproximated by the power-law distribution in the inflationary period, while\nthe distribution of absolute log-returns is well described by the exponential\ndistribution in the deflationary period.\\par To further explore these empirical\nfindings, we have introduced a model of stock markets which was proposed in\n[19,20]. In this model, the stock market is composed of two groups of traders:\n{\\it the fundamentalists}, who believe that the asset price will return to the\nfundamental price, and {\\it the interacting traders}, who can be noise traders.\nWe show through numerical simulation of the model that when the number of\ninteracting traders is greater than the number of fundamentalists, the\npower-law distribution of absolute log-returns is generated by the interacting\ntraders\u0027 herd behavior, and, inversely, when the number of fundamentalists is\ngreater than the number of interacting traders, the exponential distribution of\nabsolute log-returns is generated.",
"arxiv_id": "physics/0603139",
"authors": [
"Taisei Kaizoji"
],
"categories": [
"physics.soc-ph",
"q-fin.ST"
],
"doi": "10.1007/3-540-27296-8_16",
"journal_ref": "in T. Lux, S. Reitz, and E. Samanidou (eds.): Nonlinear Dynamics\n and Heterogeneous Intercting Agents: (Lecture Notes in Economics and\n Mathematical Systems 550), pp. 237-248, Springer-Verlag, Berlin- Heidelberg\n (2005)",
"title": "Statistical properties of absolute log-returns and a stochastic model of stock markets with heterogeneous agents",
"url": "https://arxiv.org/abs/physics/0603139"
},
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