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Complexity, Financial Markets and their Scaling Laws

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  • Indranil Mukherjee
  • Amitava Sarkar
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    Abstract

    This paper attempts to analyze financial markets characterized by, among others, by stability or the lack of it, or more directly volatility, in the framework of complexity. The seemingly uncorrelated swings of financial indices and the extreme event of a crash constitute typical phenomena of complex systems. The financial market dynamics is sometimes described using terminology from the theory of turbulence, while the financial crash is compared with a phase transition of a physical many-body system. It is possible to identify indicators for nonlinearity in financial markets, such as speculative bubbles. One also notes how quickly panic can spread in case of larger losses. These phenomena are examples of typical nonlinear processes called autocatalytic, which are characterized by conditions in which small stimuli can be strongly amplified due to the internal dynamics of the system. Financial markets can be regarded as “model” complex systems which are evolving continuously and generate huge amounts of data. It is discussed how the properties of financial markets correspond to those of a complex system. The different levels of complexity present in a financial market and the collective behaviour emerging from these markets, regarded as some kind of dynamical systems, are analyzed. The concept of auto-catalyticity is invoked to describe the power-law behaviour operating in financial markets. The concept of scaling is examined and the different scaling laws occurring in finance are discussed. Multi-fractal models of asset returns are introduced and their importance emphasized. An overview of complex systems at the beginning is provided in order to develop the concepts necessary to examine financial markets under the lens of complexity.

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    Bibliographic Info

    Paper provided by DEGIT, Dynamics, Economic Growth, and International Trade in its series DEGIT Conference Papers with number c016_008.

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    Length: 17 pages JEL Classification:
    Date of creation: Sep 2011
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    Handle: RePEc:deg:conpap:c016_008

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    1. Vandewalle, N. & Ausloos, M., 1997. "Coherent and random sequences in financial fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, Elsevier, vol. 246(3), pages 454-459.
    2. Lux, T. & M. Marchesi, . "Scaling and Criticality in a Stochastic Multi-Agent Model of a Financial Market," Discussion Paper Serie B 438, University of Bonn, Germany, revised Jul 1998.
    3. Gopikrishnan, P. & Plerou, V. & Gabaix, X. & Amaral, L.A.N. & Stanley, H.E., 2001. "Price fluctuations and market activity," Physica A: Statistical Mechanics and its Applications, Elsevier, Elsevier, vol. 299(1), pages 137-143.
    4. Louzoun, Yoram & Solomon, Sorin & Atlan, Henri & Cohen, Irun.R., 2001. "Modeling complexity in biology," Physica A: Statistical Mechanics and its Applications, Elsevier, Elsevier, vol. 297(1), pages 242-252.
    5. Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, vol. 36, pages 394.
    6. Parameswaran Gopikrishnan & Martin Meyer & Luis A Nunes Amaral & H Eugene Stanley, 1998. "Inverse Cubic Law for the Probability Distribution of Stock Price Variations," Papers cond-mat/9803374, arXiv.org, revised May 1998.
    7. Eugene F. Fama, 1963. "Mandelbrot and the Stable Paretian Hypothesis," The Journal of Business, University of Chicago Press, vol. 36, pages 420.
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