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Economic Fluctuations and Diffusion

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Author Info

  • Vasiliki Plerou
  • Parameswaran Gopikrishnan
  • Luis. A. Nunes Amaral
  • Xavier Gabaix
  • H. Eugene Stanley

Abstract

Stock price changes occur through transactions, just as diffusion in physical systems occurs through molecular collisions. We systematically explore this analogy and quantify the relation between trading activity - measured by the number of transactions $N_{\Delta t}$ - and the price change $G_{\Delta t}$, for a given stock, over a time interval $[t, t+\Delta t]$. To this end, we analyze a database documenting every transaction for 1000 US stocks over the two-year period 1994-1995. We find that price movements are equivalent to a complex variant of diffusion, where the diffusion coefficient fluctuates drastically in time. We relate the analog of the diffusion coefficient to two microscopic quantities: (i) the number of transactions $N_{\Delta t}$ in $\Delta t$, which is the analog of the number of collisions and (ii) the local variance $w^2_{\Delta t}$ of the price changes for all transactions in $\Delta t$, which is the analog of the local mean square displacement between collisions. We study the distributions of both $N_{\Delta t}$ and $w_{\Delta t}$, and find that they display power-law tails. Further, we find that $N_{\Delta t}$ displays long-range power-law correlations in time, whereas $w_{\Delta t}$ does not. Our results are consistent with the interpretation that the pronounced tails of the distribution of $G_{\Delta t} are due to $w_{\Delta t}$, and that the long-range correlations previously found for $| G_{\Delta t} |$ are due to $N_{\Delta t}$.

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File URL: http://arxiv.org/pdf/cond-mat/9912051
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Bibliographic Info

Paper provided by arXiv.org in its series Papers with number cond-mat/9912051.

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Date of creation: Dec 1999
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Publication status: Published in Phys. Rev. E. (Rapid Comm.) 62 (2000) R3023.
Handle: RePEc:arx:papers:cond-mat/9912051

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Web page: http://arxiv.org/

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Cited by:
  1. Fan, Chao & Guo, Jin-Li & Zha, Yi-Long, 2012. "Fractal analysis on human dynamics of library loans," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(24), pages 6617-6625.
  2. Gilles Zumbach, 2004. "How the trading activity scales with the company sizes in the FTSE 100," Papers cond-mat/0407769, arXiv.org.
  3. J. Doyne Farmer & Fabrizio Lillo, 2003. "On the origin of power law tails in price fluctuations," Papers cond-mat/0309416, arXiv.org, revised Jan 2004.
  4. Xavier Gabaix & Parameswaran Gopikrishnan & Vasiliki Plerou & H. Eugene Stanley, 2005. "Institutional Investors and Stock Market Volatility," NBER Working Papers 11722, National Bureau of Economic Research, Inc.
  5. Xavier Gabaix, 2009. "Power Laws in Economics and Finance," Annual Review of Economics, Annual Reviews, vol. 1(1), pages 255-294, 05.
  6. Emanuel Derman, 2002. "The Perception of Time, Risk and Return During Periods of Speculation," Papers cond-mat/0201345, arXiv.org.
  7. Christophe Schinckus, 2011. "What can econophysics contribute to financial economics?," International Review of Economics, Springer, vol. 58(2), pages 147-163, June.
  8. Sitabhra Sinha & Raj Kumar Pan, 2006. "The Power (Law) of Indian Markets: Analysing NSE and BSE trading statistics," Papers physics/0605247, arXiv.org.

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