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On the origin of power law tails in price fluctuations


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  • J. Doyne Farmer
  • Fabrizio Lillo


In a recent Nature paper, Gabaix et al. \cite{Gabaix03} presented a theory to explain the power law tail of price fluctuations. The main points of their theory are that volume fluctuations, which have a power law tail with exponent roughly -1.5, are modulated by the average market impact function, which describes the response of prices to transactions. They argue that the average market impact function follows a square root law, which gives power law tails for prices with exponent roughly -3. We demonstrate that the long-memory nature of order flow invalidates their statistical analysis of market impact, and present a more careful analysis that properly takes this into account. This makes it clear that the functional form of the average market impact function varies from market to market, and in some cases from stock to stock. In fact, for both the London Stock Exchange and the New York Stock Exchange the average market impact function grows much slower than a square root law; this implies that the exponent for price fluctuations predicted by modulations of volume fluctuations is much too big. We find that for LSE stocks the distribution of transaction volumes does not even have a power law tail. This makes it clear that volume fluctuations do not determine the power law tail of price returns.

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Bibliographic Info

Paper provided by in its series Papers with number cond-mat/0309416.

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Date of creation: Sep 2003
Date of revision: Jan 2004
Handle: RePEc:arx:papers:cond-mat/0309416

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  1. Vasiliki Plerou & Parameswaran Gopikrishnan & Luis. A. Nunes Amaral & Xavier Gabaix & H. Eugene Stanley, 1999. "Economic Fluctuations and Diffusion," Papers cond-mat/9912051,
  2. J. Doyne Farmer & Laszlo Gillemot & Fabrizio Lillo & Szabolcs Mike & Anindya Sen, 2004. "What really causes large price changes?," Quantitative Finance, Taylor & Francis Journals, vol. 4(4), pages 383-397.
  3. J. Doyne Farmer & Paolo Patelli & Ilija I. Zovko, 2003. "The Predictive Power of Zero Intelligence in Financial Markets," Papers cond-mat/0309233,, revised Feb 2004.
  4. Eric Smith & J Doyne Farmer & Laszlo Gillemot & Supriya Krishnamurthy, 2003. "Statistical theory of the continuous double auction," Quantitative Finance, Taylor & Francis Journals, vol. 3(6), pages 481-514.
  5. Parameswaran Gopikrishnan & Vasiliki Plerou & Xavier Gabaix & H. Eugene Stanley, 2000. "Statistical Properties of Share Volume Traded in Financial Markets," Papers cond-mat/0008113,
  6. V. Plerou & P. Gopikrishnan & L. A. N. Amaral & M. Meyer & H. E. Stanley, 1999. "Scaling of the distribution of price fluctuations of individual companies," Papers cond-mat/9907161,
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Cited by:
  1. Jean-Philippe Bouchaud & Julien Kockelkoren & Marc Potters, 2004. "Random walks, liquidity molasses and critical response in financial markets," Science & Finance (CFM) working paper archive 500063, Science & Finance, Capital Fund Management.
  2. Jiang, Zhi-Qiang & Zhou, Wei-Xing, 2010. "Complex stock trading network among investors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(21), pages 4929-4941.
  3. Daniel Fricke & Thomas Lux, 2013. "The Effects of a Financial Transaction Tax in an Artificial Financial Market," Kiel Working Papers 1868, Kiel Institute for the World Economy.
  4. Gao-Feng Gu & Xiong Xiong & Wei Zhang & Yong-Jie Zhang & Wei-Xing Zhou, 2014. "Empirical properties of inter-cancellation durations in the Chinese stock market," Papers 1403.3478,
  5. Daniel C. Wagner & Thilo A. Schmitt & Rudi Sch\"afer & Thomas Guhr & Dietrich E. Wolf, 2014. "Analysis of a decision model in the context of equilibrium pricing and order book pricing," Papers 1404.7356,
  6. Wei-Xing Zhou, 2007. "Universal price impact functions of individual trades in an order-driven market," Papers 0708.3198,, revised Apr 2008.
  7. Hokky Situngkir & Yohanes Surya, 2004. "Stylized Statistical Facts of Indonesian Financial Data: Empirical Study of Several Stock Indexes in Indonesia," Finance 0405005, EconWPA.
  8. Thomas Lux, 2006. "Financial Power Laws: Empirical Evidence, Models, and Mechanism," Working Papers wpn06-08, Warwick Business School, Finance Group.
  9. Stanley, H.E. & Gabaix, Xavier & Gopikrishnan, Parameswaran & Plerou, Vasiliki, 2007. "Economic fluctuations and statistical physics: Quantifying extremely rare and less rare events in finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 382(1), pages 286-301.
  10. James B. Glattfelder & Thomas Bisig & Richard B. Olsen, 2014. "R&D Strategy Document," Papers 1405.6027,
  11. Bacry, Emmanuel & Kozhemyak, Alexey & Muzy, Jean-Fran├žois, 2006. "Are asset return tail estimations related to volatility long-range correlations?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(1), pages 119-126.
  12. Stanley, H. Eugene & Plerou, Vasiliki & Gabaix, Xavier, 2008. "A statistical physics view of financial fluctuations: Evidence for scaling and universality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(15), pages 3967-3981.
  13. Levy, Moshe, 2008. "Stock market crashes as social phase transitions," Journal of Economic Dynamics and Control, Elsevier, vol. 32(1), pages 137-155, January.
  14. Gao-Feng Gu & Xiong Xiong & Yong-Jie Zhang & Wei Chen & Wei Zhang & Wei-Xing Zhou, 2014. "Stylized facts of price gaps in limit order books: Evidence from Chinese stocks," Papers 1405.1247,
  15. David Morton de Lachapelle & Damien Challet, 2009. "Turnover, account value and diversification of real traders: evidence of collective portfolio optimizing behavior," Papers 0912.4723,, revised Jun 2010.
  16. Lux, Thomas, 2006. "Financial power laws: Empirical evidence, models, and mechanism," Economics Working Papers 2006,12, Christian-Albrechts-University of Kiel, Department of Economics.
  17. Sitabhra Sinha & Raj Kumar Pan, 2006. "The Power (Law) of Indian Markets: Analysing NSE and BSE trading statistics," Papers physics/0605247,
  18. Ni, Xiao-Hui & Jiang, Zhi-Qiang & Gu, Gao-Feng & Ren, Fei & Chen, Wei & Zhou, Wei-Xing, 2010. "Scaling and memory in the non-Poisson process of limit order cancelation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(14), pages 2751-2761.


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