dorsal/arxiv
View SchemaA Precursor of Market Crashes
| Authors | Taisei Kaizoji |
|---|---|
| Categories | |
| ArXiv ID | physics/0510055 |
| URL | https://arxiv.org/abs/physics/0510055 |
| DOI | 10.1140/epjb/e2006-00142-9 |
| Journal | European Physical Journal B50 (2006) 123-127 |
Abstract
In this paper, we quantitatively investigate the properties of a statistical ensemble of stock prices. We focus attention on the relative price defined as $ X(t) = S(t)/S(0) $, where $ S(0) $ is the initial price. We selected approximately 3200 stocks traded on the Japanese Stock Exchange and formed a statistical ensemble of daily relative prices for each trading day in the 3-year period from January 4, 1999 to December 28, 2001, corresponding to the period in which the {\it internet Bubble} formed and {\it crashes} in the Japanese stock market. We found that the upper tail of the complementary cumulative distribution function of the ensemble of the relative prices in the high value of the price is well described by a power-law distribution, $ P(S>x) \sim x^{-\alpha} $, with an exponent that moves over time. Furthermore, we found that as the power-law exponents $ \alpha $ approached {\it two}, the bubble burst. It is reasonable to assume that when the power-law exponents approached {\it two}, it indicates the bubble is about to burst. PACS: 89.65.Gh; Keywords: Market crashes, Power law, Precursor
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"abstract": "In this paper, we quantitatively investigate the properties of a statistical\nensemble of stock prices. We focus attention on the relative price defined as $\nX(t) = S(t)/S(0) $, where $ S(0) $ is the initial price. We selected\napproximately 3200 stocks traded on the Japanese Stock Exchange and formed a\nstatistical ensemble of daily relative prices for each trading day in the\n3-year period from January 4, 1999 to December 28, 2001, corresponding to the\nperiod in which the {\\it internet Bubble} formed and {\\it crashes} in the\nJapanese stock market. We found that the upper tail of the complementary\ncumulative distribution function of the ensemble of the relative prices in the\nhigh value of the price is well described by a power-law distribution, $ P(S\u003ex)\n\\sim x^{-\\alpha} $, with an exponent that moves over time. Furthermore, we\nfound that as the power-law exponents $ \\alpha $ approached {\\it two}, the\nbubble burst. It is reasonable to assume that when the power-law exponents\napproached {\\it two}, it indicates the bubble is about to burst.\n PACS: 89.65.Gh; Keywords: Market crashes, Power law, Precursor",
"arxiv_id": "physics/0510055",
"authors": [
"Taisei Kaizoji"
],
"categories": [
"physics.soc-ph",
"physics.data-an",
"q-fin.ST"
],
"doi": "10.1140/epjb/e2006-00142-9",
"journal_ref": "European Physical Journal B50 (2006) 123-127",
"title": "A Precursor of Market Crashes",
"url": "https://arxiv.org/abs/physics/0510055"
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