Progress in physical properties of Chinese stock markets

Abstract

In the past two decades, statistical physics was brought into the field of finance, applying new methods and concepts to financial time series and developing a new interdiscipline “econophysics”. In this review, we introduce several commonly used methods for stock time series in econophysics including distribution functions, correlation functions, detrended fluctuation analysis method, detrended moving average method, and multifractal analysis. Then based on these methods, we review some statistical properties of Chinese stock markets including scaling behavior, long-term correlations, cross-correlations, leverage effects, antileverage effects, and multifractality. Last, based on an agent-based model, we develop a new option pricing model — financial market model that shows a good agreement with the prices using real Shanghai Index data. This review is helpful for people to understand and research statistical physics of financial markets.

Keywords

econophysics / Chinese stock market / statistical method / statistical physics

References

[1] J. D. Farmer, Physicists attempt to scale the ivory towers of finance, Comput. Sci. Eng., 1999, 1(6): 26

[2] B. Mandelbrot, The variation of certain speculative prices, J. Buss., 1963, 36(4): 394

[3] E. Fama, The behavior of stock-market prices, J. Buss., 1965, 38(1): 34

[4] W. X. Zhou, A Guide to Econophysics, Shanghai: Shanghai University of Finance and Economics Press, 2007 (in Chinese)

[5] R. N. Mantegna and H. E. Stanley, Scaling behaviour in the dynamics of an economic index, Nature, 1995, 376(6535): 46

[6] V. Plerou, P. Gopikrishnan, L. N. Amaral, M. Meyer, and H. E. Stanley, Scaling of the distribution of price fluctuations of individual companies, Phys. Rev. E, 1999, 60(6): 6519

[7] P. Gopikrishnan, V. Plerou, L. N. Amaral, M. Meyer, and H. E. Stanley, Scaling of the distribution of fluctuations of financial market indices, Phys. Rev. E, 1999, 60(5): 5305

[8] J. P. Bouchaud and M. Potters, Theory of Financial Risk, Cambridge: Cambridge University Press, 2000

[9] K. Matia, L. A. N. Amaral, S. P. Goodwin, and H. E. Stanley, Different scaling behaviors of commodity spot and future prices, Phys. Rev. E, 2002, 66(4): 045103

[10] T. Qiu, B. Zheng, F. Ren, and S. Trimper, Statistical properties of German Dax and Chinese indices, Physica A, 2007, 378(2): 387

[11] C. Yan, J. W. Zhang, Y. Zhang, and Y. N. Tang, Power-law properties of Chinese stock market, Physica A, 2005, 353: 425

[12] J. W. Zhang, Y. Zhang, and H. Kleinert, Power tails of index distributions in Chinese stock market, Physica A, 2007, 377(1): 166

[13] K. Yamasaki, L. Muchnik, S. Havlin, A. Bunde, and H. E. Stanley, Scaling and memory in volatility return intervals in financial markets, Proc. Natl. Acad. Sci. USA, 2005, 102(26): 9424

[14] C. P. Zhu, X. T. Liu, and Z. M. Gu, Flat-head powerlaw, size-independent clustering and scaling of coevolutionary scale-free networks, Front. Phys., 2011, 6(3): 337

[15] J. L. Ma and F. T. Ma, Solitary wave solutions of nonlinear financial markets: Data-modeling-conceptpracticing, Front. Phys. China, 2007, 2(3): 368

[16] W. Wan and J. W. Zhang, Long-term memory of the returns in the Chinese stock indices, Front. Phys. China, 2008, 3(4): 489

[17] W. C. Zhou, H. C. Xu, Z. Y. Cai, J. R. Wei, X. Y. Zhu, W. Wang, L. Zhao, and J. P. Huang, Peculiar statistical properties of Chinese stock indices in bull and bear market phases, Physica A, 2009, 388(6): 891

[18] G. F. Gu, W. Chen, and W. X. Zhou, Empirical distributions of Chinese stock returns at different microscopic timescales, Physica A, 2008, 387(2–3): 495

[19] M. Y. Bai and H. B. Zhu, Power law and multiscaling properties of the Chinese stock market, Physica A, 2010, 389(9): 1883

[20] G. H. Mu, W. Chen, J. Kertesz, and W. X. Zhou, Preferred numbers and the distribution of trade sizes and trading volumes in the Chinese stock market, Eur. Phys. J. B, 2009, 68(1): 145

[21] J. Shen and B. Zheng, Cross-correlation in financial dynamics, Europhys. Lett., 2009, 86(4): 48005

[22] T. Qiu, B. Zheng, F. Ren, and S. Trimper, Return-volatility correlation in financial dynamics, Phys. Rev. E, 2006, 73(6): 065103 (R)

[23] W. X. Zhou, The components of empirical multifractality in financial returns, Europhys. Lett., 2009, 88(2): 28004

[24] Y. P. Ruan and W. X. Zhou, Long-term correlations and multifractal nature in the intertrade durations of a liquid Chinese stock and its warrant, Physica A, 2011, 390(9): 1646

[25] G. H. Mu, W. X. Zhou, W. Chen, and J. Kertesz, Longterm correlations and multifractality in trading volume for Chinese stocks, Physics Procedia, 2010, 3(5): 1631

[26] G. F. Gu and W. X. Zhou, Statistical properties of daily ensemble variables in the Chinese stock markets, Physica A, 2007, 383(2): 497

[27] T. Qiu, G. Chen, L. X. Zhong, and X. W. Lei, Memory effect and multifractality of cross-correlations in financial markets, Physica A, 2011, 390(5): 828

[28] G. X. Du and X. X. Ning, Multifractal properties of Chinese stock market in Shanghai, Physica A, 2008, 387(1): 261

[29] Y. Yuan, X. T. Zhuang, and Z. Y. Liu, Price-volume multifractal analysis and its application in Chinese stock markets, Physica A, 2012, 391(12): 3484

[30] S. P. Chen and L. Y. He, Multifractal spectrum analysis of nonlinear dynamical mechanisms in China’s agricultural futures markets, Physica A, 2010, 389(7): 1434

[31] F. Ren, G. F. Gu, and W. X. Zhou, Scaling and memory in the return intervals of realized volatility, Physica A, 2009, 388(22): 4787

[32] F. Ren and W. X. Zhou, Multiscaling behavior in the volatility return intervals of Chinese indices, Europhys. Lett., 2008, 84(6): 68001

[33] F. Ren, L. Guo, and W. X. Zhou, Statistical properties of volatility return intervals of Chinese stocks, Physica A, 2009, 388(6): 881

[34] T. Qiu, L. X. Zhong, G. Chen, and X. R. Wu, Statistical properties of trading volume of Chinese stocks, Physica A, 2009, 388(12): 2427

[35] X. Q. Sun, X. Q. Cheng, H. W. Shen, and Z. Y. Wang, Statistical properties of trading activity in Chinese stock market, Physics Procedia, 2010, 3(5): 1699

[36] Z. Q. Jiang, W. Chen, and W. X. Zhou, Scaling in the distribution of intertrade durations of Chinese stocks, Physica A, 2008, 387(23): 5818

[37] V. Plerou, P. Gopikrishnan, B. Rosenow, L. N. Amaral, and H. E. Stanley, Universal and nonuniversal properties of cross correlations in financial time series, Phys. Rev. Lett., 1999, 83(7): 1471

[38] P. Gopikrishnan, B. Rosenow, V. Plerou, and H. E. Stanley, Quantifying and interpreting collective behavior in financial markets, Phys. Rev. E, 2001, 64(3): 035106

[39] V. Plerou, P. Gopikrishnan, B. Rosenow, L. N. Amaral, T. Guhr, and H. E. Stanley, Random matrix approach to cross correlations in financial data, Phys. Rev. E, 2002, 65(6): 066126

[40] K. G. D. R. Nilantha, Ranasinghe, and P. K. C. Malmini, Eigenvalue density of cross-correlations in Sri Lankan financial market, Physica A, 2007, 378(2): 345

[41] E. Alessio, A. Carbone, G. Castelli, and V. Frappietro, Second-order moving average and scaling of stochastic time series, Eur. Phys. J. B, 2002, 27(2): 197

[42] S. Arianos and A. Carbone, Detrending moving average algorithm: A closed-form approximation of the scaling law, Physica A, 2007, 382(1): 9

[43] A. Carbone, Detrending moving average algorithm: A brief review, in: Proceeding of Science and Technology for Humanity, IEEE Toronto International Conference, 2009: 691

[44] Y. H. Shao, G. F. Gu, Z. Q. Jiang, W. X. Zhou, and D. Sornette, Comparing the performance of FA, DFA and DMA using different synthetic long-range correlated time series, Scientific Reports, 2012, 2: 835

[45] G. F. Gu and W. X. Zhou, Detrending moving average algorithm for multifractals, Phys. Rev. E, 2010, 82(1): 011136

[46] B. Podobnik and H. E. Stanley, Detrended cross-correlation analysis: A new method for analyzing two nonstationary time series, Phys. Rev. Lett., 2008, 100(8): 084102

[47] S. Arianos and A. Carbone, Cross-correlation of long-range correlated series, Journal of Statistical Mechanism – Theory and Experiment, 2009: P03037

[48] W. X. Zhou, Multifractal detrended cross-correlation analysis for two nonstationary signals, Phys. Rev. E, 2008, 77(6): 066211

[49] Z. Q. Jiang and W. X. Zhou, Multifractal detrending moving average cross-correlation analysis, Phys. Rev. E, 2011, 84(1): 016106

[50] L. Bachelier, Theorie de la, Paris: Gauthier-Villars, 1900

[51] R. N. Mantegna and H. E. Stanley, Introduction to Econophysics: Correlations and Complexity in Finance, Cambridge: Cambridge University Press, 1999

[52] J. P. Bouchaud and D. Sornette, The Black-Scholes option pricing problem in mathematical finance: Generalization and extensions for a large class of stochastic processes, J. Phys. I France, 1994, 4: 863

[53] G. H. Mu and W. X. Zhou, Tests of nonuniversality of the stock return distributions in an emerging market, Phys. Rev. E, 2010, 82(6): 066103

[54] C. K. Peng, S. Havlin, H. E. Stanley, and A. L. Goldberger, Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series, Chaos, 1995, 5(1): 82

[55] C. K. Peng, S. V. Buldyrev, S. Havlin, M. Simons, H. E. Stanley, and A. L. Goldberger, Mosaic organization of DNA nucleotides, Phys. Rev. E, 1994, 49(2): 1685

[56] K. Matia, Y. Ashkenazy, and H. E. Stanley, Multifractal properties of price fluctuations of stocks and commodities, Europhys. Lett., 2003, 61(3): 422

[57] S. Ghashghaie, W. Breymann, J. Peinke, P. Talkner, and Y. Dodge, Turbulent cascades in foreign exchange markets, Nature, 1996, 381(6585): 767

[58] R. N. Mantegna and H. E. Stanley, Turbulence and financial markets, Nature, 1996, 383(6601): 587

[59] B. B. Mandelbrot, A multifractal walk down Wall Street, Sci. Am., 1999, 280(2): 70

[60] N. F. Johnson, P. Jefferies, and P. M. Hui, Financial Market Complexity, Oxford: Oxford University Press, s

[61] J. C. Hull, Options, Futures, and Other Derivatives, 7th Ed., New Jersey: Prentice Education, Inc., 2009

[62] Z. Bodie, A. Kane, and A. J. Marcus, Investments, 8th Ed., US: McGraw-Hill Education, 2009

[63] F. Black and M. Scholes, The pricing of options and corporate liabilities, J. Polit. Econ., 1973, 81(3): 637

[64] R. C. Merton, Theory of rational option pricing, Bell J. Econ. Manage. Sci., 1973, 4(1): 141

[65] C. H. Yeung, K. M.Wong, and Y. C. Zhang, Models of financial markets with extensive participation incentives, Phys. Rev. E, 2008, 77(2): 026107

[66] W. Wang, Y. Chen, and J. P. Huang, Heterogeneous preferences, decision-making capacity and phase transitions in a complex adaptive system, Proc. Natl. Acad. Sci. USA, 2009, 106(21): 8423

[67] L. Zhao, G. Yang, W. Wang, Y. Chen, J. P. Huang, H. Ohashi, and H. E. Stanley, Herd behavior in a complex adaptive system, Proc. Natl. Acad. Sci. USA, 2011, 108(37): 15058

[68] Y. Liang, K. N. An, G. Yang, and J. P. Huang, Contrarian behavior in a complex adaptive system, Phys. Rev. E, 2013, 87(1): 012809

[69] K. Y. Song, K. N. An, G. Yang, and J. P. Huang, Riskreturn relationship in a complex adaptive system, PLoS ONE, 2012, 7(3): e33588

[70] W. Z. Zheng, Y. Liang, and J. P. Huang, Equilibrium state and non-equilibrium steady state in an isolated human system, Front. Phys., 2013 (in press)

[71] Y. Liang and J. P. Huang, Robustness of critical points in a complex adaptive system: Effects of hedge behavior, Front. Phys., 2013

[72] D. Challet, A. Chessa, M. Marsili, and Y. C. Zhang, From minority games to real markets, Quant. Finance, 2001, 1(1): 168

[73] R. Cont and J. P. Bouchaud, Herd behavior and aggregate fluctuations in financial markets, Macroeconomic Dynamics, 2000, 4(02): 170

[74] C. H. Hommes, Modeling the stylized facts in finance through simple nonlinear adaptive systems, Proc. Natl. Acad. Sci. USA, 2002, 99(90003): 7221

[75] V. Al., M. Cristelli, L. Pietronero, and A. Zaccaria, Minimal agent based model for financial markets I, Eur. Phys. J. B, 2009, 67(3): 385

[76] T. Lux and M. Marchesi, Scaling and criticality in a stochastic multi-agent model of a financial market, Nature, 1999, 397(6719): 498

[77] S. Thurner, J. D. Farmer, and J. Geanakoplos, Leverage causes fat tails and clustered volatility, Quant. Finance, 2012, 12(5): 695

[78] J. Wiesinger, D. Sornette, and J. Satinover, Reverse engineering financial markets with majority and minority games using genetic algorithms, Comput. Econ., 2013, 41(4): 475

[79] S. Mike and J. D. Farmer, An empirical behavioral model of liquidity and volatility, J. Econ. Dyn. Control, 2008, 32(1): 200

[80] G. F. Gu and W. X. Zhou, Emergence of long memory in stock volatility from a modified Mike-Farmer model, Europhys. Lett., 2009, 86(4): 48002

[81] J. R. Wei and J. P. Huang, An exotic long-term pattern in stock price dynamics, PLoS ONE, 2012, 7(12): e51666

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