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CN 34-1054/N

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Study on the self-organized financial model based on scale-free networks

  • Department of Electronical Science and Technology, University of Science and Technology of China, Hefei 230027, China

Cite this:
https://doi.org/10.3969/j.issn.0253-2778.2014.01.009
  • Received Date: 28 April 2013
  • Accepted Date: 10 May 2013
  • Rev Recd Date: 10 May 2013
  • Publish Date: 30 January 2014
    Abstract

  • Abstract

    For a series of grid-based Cont-Bouchaud (CB) models unable to correctly represent the heterogeneity of interactions among investors in the real financial market, an improved evolutionary model constrained by trading rules was proposed based on the percolation theory on scale-free networks. The time series of price fluctuations generated by the model was similar to the stock index in the real financial markets. For instances, the probability distributions of returns showed the sharp peak and fat tail, and their peak values restricted to the time scales obey the power-law behavior, which suggests that the time series of price fluctuations evolves in a self-similarity way. The clustering behavior of volatility shows that there are large fluctuations and long-range correlations in the evolutionary process. These statistical properties of return and volatility empirically are consistent with the real financial markets, indicating the effectiveness of the improved model.

    Abstract

    For a series of grid-based Cont-Bouchaud (CB) models unable to correctly represent the heterogeneity of interactions among investors in the real financial market, an improved evolutionary model constrained by trading rules was proposed based on the percolation theory on scale-free networks. The time series of price fluctuations generated by the model was similar to the stock index in the real financial markets. For instances, the probability distributions of returns showed the sharp peak and fat tail, and their peak values restricted to the time scales obey the power-law behavior, which suggests that the time series of price fluctuations evolves in a self-similarity way. The clustering behavior of volatility shows that there are large fluctuations and long-range correlations in the evolutionary process. These statistical properties of return and volatility empirically are consistent with the real financial markets, indicating the effectiveness of the improved model.
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    • References(16)
  • [1]
    Mantegna R N, Stanley H E. Scaling behavior in the dynamics of an economic index[J]. Nature, 1995, 376: 46-49.
    [2]
    Galluccio S, Caldarelli G, Marsili M, et al. Scaling in currency exchange[J]. Physica A, 1997, 245: 423-436.
    [3]
    Gopikrishnan P, Plerou V, Nunes Amaral L A, et al. Scaling of the distribution of fluctuations of financial market indices[J]. Physics Review E, 1999, 60(5): 5 305-5 316.
    [4]
    Liu Y, Gopikrishnan P, Cizeau P, et al. Statistical properties of the volatility of price fluctuations[J]. Physics Review E, 1999, 60(2): 1 390-1 400.
    [5]
    Wang B H, Hui P M. The distribution and scaling of fluctuations for Hang Seng index in Hong Kong stock market [J]. European Physics Journal B, 2001, 20: 573-579.
    [6]
    Cont R, Bouchaud J P. Herd behavior and aggregate fluctuations in financial markets[J]. Macroeconomic Dynamics, 2000, 4(2):170-196.
    [7]
    Lux T, Marchesi M. Scaling and criticality in a stochastic multi-agent model of a financial market[J]. Nature, 1999, 397(11): 498-500.
    [8]
    LeBaron B. Evolution and time horizons in an agent-based stock market[J]. Macroeconomic Dynamics, 2001, 5(2): 225-254.
    [9]
    Wang J, Yang C X, Zhou P L, et al. Evolutionary percolation model of stock market with variable agent number[J]. Physica A, 2005, 354: 505-517.
    [10]
    Kahneman D, Tversky A. Prospect theory: An analysis of decision under risk[J]. Econometrica, 1979, 47(2): 263-291.
    [11]
    杨春霞, 王杰, 周涛, 等. 基于自组织逾渗的金融市场模型[J]. 科学通报, 2005, 50(20): 2 309-2 313.
    [12]
    ZHOU Yan-bo, CAI Shi-min, ZHOU Pei-ling. Scale-free properties of financial markets[J]. Journal of University of Science and Technology of China, 2009, 39(8): 880-884.
    周艳波, 蔡世民, 周佩玲. 金融市场的无标度特征研究[J]. 中国科学技术大学学报, 2009, 39(8): 880-884.
    [13]
    Cai S M, Zhou Y B, Zhou T, et al. Hierarchical organization and disassortative mixing of correlation-based weighted financial networks[J]. International Journal of Modern Physics C, 2010, 21(3): 433-441.
    [14]
    Barabsi A L, Albert R. Emergence of scaling in random networks[J]. Science, 1999, 286(5439): 509-512.
    [15]
    Cavalcante F S A, Morira A A, Costa U M S, et al. Self-organized percolation growth in regular and disordered lattices[J]. Physica A, 2002, 311(3-4): 313-319.
    [16]
    Dorogovtsev S N, Mendes J F F, Samukhin A N. Structure of growing networks with preferential linking[J]. Physical Review Letters, 2000, 85(21): 4 633-4 636.
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    [1]
    Mantegna R N, Stanley H E. Scaling behavior in the dynamics of an economic index[J]. Nature, 1995, 376: 46-49.
    [2]
    Galluccio S, Caldarelli G, Marsili M, et al. Scaling in currency exchange[J]. Physica A, 1997, 245: 423-436.
    [3]
    Gopikrishnan P, Plerou V, Nunes Amaral L A, et al. Scaling of the distribution of fluctuations of financial market indices[J]. Physics Review E, 1999, 60(5): 5 305-5 316.
    [4]
    Liu Y, Gopikrishnan P, Cizeau P, et al. Statistical properties of the volatility of price fluctuations[J]. Physics Review E, 1999, 60(2): 1 390-1 400.
    [5]
    Wang B H, Hui P M. The distribution and scaling of fluctuations for Hang Seng index in Hong Kong stock market [J]. European Physics Journal B, 2001, 20: 573-579.
    [6]
    Cont R, Bouchaud J P. Herd behavior and aggregate fluctuations in financial markets[J]. Macroeconomic Dynamics, 2000, 4(2):170-196.
    [7]
    Lux T, Marchesi M. Scaling and criticality in a stochastic multi-agent model of a financial market[J]. Nature, 1999, 397(11): 498-500.
    [8]
    LeBaron B. Evolution and time horizons in an agent-based stock market[J]. Macroeconomic Dynamics, 2001, 5(2): 225-254.
    [9]
    Wang J, Yang C X, Zhou P L, et al. Evolutionary percolation model of stock market with variable agent number[J]. Physica A, 2005, 354: 505-517.
    [10]
    Kahneman D, Tversky A. Prospect theory: An analysis of decision under risk[J]. Econometrica, 1979, 47(2): 263-291.
    [11]
    杨春霞, 王杰, 周涛, 等. 基于自组织逾渗的金融市场模型[J]. 科学通报, 2005, 50(20): 2 309-2 313.
    [12]
    ZHOU Yan-bo, CAI Shi-min, ZHOU Pei-ling. Scale-free properties of financial markets[J]. Journal of University of Science and Technology of China, 2009, 39(8): 880-884.
    周艳波, 蔡世民, 周佩玲. 金融市场的无标度特征研究[J]. 中国科学技术大学学报, 2009, 39(8): 880-884.
    [13]
    Cai S M, Zhou Y B, Zhou T, et al. Hierarchical organization and disassortative mixing of correlation-based weighted financial networks[J]. International Journal of Modern Physics C, 2010, 21(3): 433-441.
    [14]
    Barabsi A L, Albert R. Emergence of scaling in random networks[J]. Science, 1999, 286(5439): 509-512.
    [15]
    Cavalcante F S A, Morira A A, Costa U M S, et al. Self-organized percolation growth in regular and disordered lattices[J]. Physica A, 2002, 311(3-4): 313-319.
    [16]
    Dorogovtsev S N, Mendes J F F, Samukhin A N. Structure of growing networks with preferential linking[J]. Physical Review Letters, 2000, 85(21): 4 633-4 636.
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