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Economic Fluctuations and Diffusion


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


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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Paper provided by 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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Cited by:
  1. Gilles Zumbach, 2004. "How the trading activity scales with the company sizes in the FTSE 100," Papers cond-mat/0407769,
  2. Xavier Gabaix, 2009. "Power Laws in Economics and Finance," Annual Review of Economics, Annual Reviews, Annual Reviews, vol. 1(1), pages 255-294, 05.
  3. 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.
  4. Emanuel Derman, 2002. "The Perception of Time, Risk and Return During Periods of Speculation," Papers cond-mat/0201345,
  5. 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.
  6. Sitabhra Sinha & Raj Kumar Pan, 2006. "The Power (Law) of Indian Markets: Analysing NSE and BSE trading statistics," Papers physics/0605247,
  7. Christophe Schinckus, 2011. "What can econophysics contribute to financial economics?," International Review of Economics, Springer, vol. 58(2), pages 147-163, June.
  8. J. Doyne Farmer & Fabrizio Lillo, 2003. "On the origin of power law tails in price fluctuations," Papers cond-mat/0309416,, revised Jan 2004.


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