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Self-organization of price fluctuation distribution in evolving markets

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  • Raj Kumar Pan
  • Sitabhra Sinha

Abstract

Financial markets can be seen as complex systems in non-equilibrium steady state, one of whose most important properties is the distribution of price fluctuations. Recently, there have been assertions that this distribution is qualitatively different in emerging markets as compared to developed markets. Here we analyse both high-frequency tick-by-tick as well as daily closing price data to show that the price fluctuations in the Indian stock market, one of the largest emerging markets, have a distribution that is identical to that observed for developed markets (e.g., NYSE). In particular, the cumulative distribution has a long tail described by a power law with an exponent $\alpha \approx 3$. Also, we study the historical evolution of this distribution over the period of existence of the National Stock Exchange (NSE) of India, which coincided with the rapid transformation of the Indian economy due to liberalization, and show that this power law tail has been present almost throughout. We conclude that the ``inverse cubic law'' is a truly universal feature of a financial market, independent of its stage of development or the condition of the underlying economy.

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  • Raj Kumar Pan & Sitabhra Sinha, 2006. "Self-organization of price fluctuation distribution in evolving markets," Papers physics/0606213, arXiv.org, revised May 2007.
    • Handle: RePEc:arx:papers:physics/0606213
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    References listed on IDEAS

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    1. Bouchaud,Jean-Philippe & Potters,Marc, 2003. "Theory of Financial Risk and Derivative Pricing," Cambridge Books, Cambridge University Press, number 9780521819169, November.
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    Cited by:

    1. T. T. Chen & B. Zheng & Y. Li & X. F. Jiang, 2017. "New approaches in agent-based modeling of complex financial systems," Papers 1703.06840, arXiv.org.
    2. Jiang, Xiong-Fei & Zheng, Bo & Ren, Fei & Qiu, Tian, 2017. "Localized motion in random matrix decomposition of complex financial systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 154-161.
    3. Chakraborty, Abhijit & Easwaran, Soumya & Sinha, Sitabhra, 2018. "Deviations from universality in the fluctuation behavior of a heterogeneous complex system reveal intrinsic properties of components: The case of the international currency market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 599-610.
    4. Gu, Gao-Feng & Chen, Wei & Zhou, Wei-Xing, 2008. "Empirical distributions of Chinese stock returns at different microscopic timescales," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(2), pages 495-502.
    5. Peng Liu & Yanyan Zheng, 2022. "Precision measurement of the return distribution property of the Chinese stock market index," Papers 2209.08521, arXiv.org, revised Nov 2023.
    6. F. Y. Ouyang & B. Zheng & X. F. Jiang, 2014. "Spatial and temporal structures of four financial markets in Greater China," Papers 1402.1046, arXiv.org.
    7. Tabak, B.M. & Takami, M.Y. & Cajueiro, D.O. & Petitinga, A., 2009. "Quantifying price fluctuations in the Brazilian stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(1), pages 59-62.
    8. Tetsuya Takaishi, 2021. "Time-varying properties of asymmetric volatility and multifractality in Bitcoin," PLOS ONE, Public Library of Science, vol. 16(2), pages 1-21, February.
    9. Ouyang, F.Y. & Zheng, B. & Jiang, X.F., 2014. "Spatial and temporal structures of four financial markets in Greater China," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 402(C), pages 236-244.
    10. Pan, Raj Kumar & Sinha, Sitabhra, 2008. "Inverse-cubic law of index fluctuation distribution in Indian markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(8), pages 2055-2065.
    11. Sitabhra Sinha & Uday Kovur, 2013. "Uncovering the network structure of the world currency market: Cross-correlations in the fluctuations of daily exchange rates," Papers 1305.0239, arXiv.org.
    12. Tetsuya Takaishi, 2021. "Time-varying properties of asymmetric volatility and multifractality in Bitcoin," Papers 2102.07425, arXiv.org.

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