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Modeling interactions of trading volumes in financial dynamics

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  • Ren, F.
  • Zheng, B.
  • Chen, P.

Abstract

A dynamic herding model with interactions of trading volumes is introduced. At time t, an agent trades with a probability, which depends on the ratio of the total trading volume at time t−1 to its own trading volume at its last trade. The price return is determined by the volume imbalance and number of trades. The model can reproduce the power-law distributions of the trading volume, number of trades and price return, and the probable relation between them. The exponents are tunable by adjusting the values of the parameters, but show slight deviation from those revealed in empirical studies. Moreover, the time series generated are long-range correlated. We demonstrate that the results are rather robust, and do not depend on the particular form of the trading probability.

Suggested Citation

  • Ren, F. & Zheng, B. & Chen, P., 2010. "Modeling interactions of trading volumes in financial dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(14), pages 2744-2750.
    • Handle: RePEc:eee:phsmap:v:389:y:2010:i:14:p:2744-2750
    DOI: 10.1016/j.physa.2010.02.039
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    References listed on IDEAS

    as
    1. Sanmay Das, 2005. "A learning market-maker in the Glosten-Milgrom model," Quantitative Finance, Taylor & Francis Journals, vol. 5(2), pages 169-180.
    2. Hasbrouck, Joel, 1991. "Measuring the Information Content of Stock Trades," Journal of Finance, American Finance Association, vol. 46(1), pages 179-207, March.
    3. Wood, Robert A & McInish, Thomas H & Ord, J Keith, 1985. "An Investigation of Transactions Data for NYSE Stocks," Journal of Finance, American Finance Association, vol. 40(3), pages 723-739, July.
    4. 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, arXiv.org.
    5. 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.
    6. Marcus Lim & Richard Coggins, 2005. "The immediate price impact of trades on the Australian Stock Exchange," Quantitative Finance, Taylor & Francis Journals, vol. 5(4), pages 365-377.
    7. Stauffer, Dietrich & Sornette, Didier, 1999. "Self-organized percolation model for stock market fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 271(3), pages 496-506.
    8. Philipp Weber & Bernd Rosenow, 2006. "Large stock price changes: volume or liquidity?," Quantitative Finance, Taylor & Francis Journals, vol. 6(1), pages 7-14.
    9. Yanhui Liu & Parameswaran Gopikrishnan & Pierre Cizeau & Martin Meyer & Chung-Kang Peng & H. Eugene Stanley, 1999. "The statistical properties of the volatility of price fluctuations," Papers cond-mat/9903369, arXiv.org, revised Mar 1999.
    10. Karpoff, Jonathan M., 1987. "The Relation between Price Changes and Trading Volume: A Survey," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 22(1), pages 109-126, March.
    11. Irene Giardina & Jean-Philippe Bouchaud & Marc M'ezard, 2001. "Microscopic Models for Long Ranged Volatility Correlations," Papers cond-mat/0105076, arXiv.org.
    12. Cont, Rama & Bouchaud, Jean-Philipe, 2000. "Herd Behavior And Aggregate Fluctuations In Financial Markets," Macroeconomic Dynamics, Cambridge University Press, vol. 4(2), pages 170-196, June.
    13. Ren, F. & Zheng, B. & Lin, H. & Wen, L.Y. & Trimper, S., 2005. "Persistence probabilities of the German DAX and Shanghai Index," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 350(2), pages 439-450.
    14. Qiu, T. & Zhong, L.X. & Chen, G. & Wu, X.R., 2009. "Statistical properties of trading volume of Chinese stocks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(12), pages 2427-2434.
    15. Gontis, V. & Kaulakys, B., 2004. "Multiplicative point process as a model of trading activity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 343(C), pages 505-514.
    16. Gabaix, Xavier & Gopikrishnan, Parameswaran & Plerou, Vasiliki & Stanley, Eugene, 2007. "A unified econophysics explanation for the power-law exponents of stock market activity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 382(1), pages 81-88.
    17. Challet, D. & Zhang, Y.-C., 1997. "Emergence of cooperation and organization in an evolutionary game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 246(3), pages 407-418.
    18. Ren, F. & Zheng, B. & Qiu, T. & Trimper, S., 2006. "Score-dependent payoffs and Minority Games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 371(2), pages 649-657.
    19. Vygintas Gontis & Bronislovas Kaulakys, 2003. "Multiplicative point process as a model of trading activity," Papers cond-mat/0303089, arXiv.org, revised Dec 2004.
    20. Vasiliki Plerou & Parameswaran Gopikrishnan & Luis. A. Nunes Amaral & Xavier Gabaix & H. Eugene Stanley, 1999. "Economic Fluctuations and Diffusion," Papers cond-mat/9912051, arXiv.org.
    21. Lobato, Ignacio N & Velasco, Carlos, 2000. "Long Memory in Stock-Market Trading Volume," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(4), pages 410-427, October.
    22. Fabrizio Lillo & J. Doyne Farmer & Rosario N. Mantegna, 2003. "Master curve for price-impact function," Nature, Nature, vol. 421(6919), pages 129-130, January.
    23. Irene Giardina & Jean-Philippe Bouchaud & Marc Mezard, 2001. "Microscopic models for long ranged volatility correlations," Science & Finance (CFM) working paper archive 500024, Science & Finance, Capital Fund Management.
    24. Giardina, Irene & Bouchaud, Jean-Philippe & Mézard, Marc, 2001. "Microscopic models for long ranged volatility correlations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 299(1), pages 28-39.
    25. Xavier Gabaix & Parameswaran Gopikrishnan & Vasiliki Plerou & H. Eugene Stanley, 2003. "A theory of power-law distributions in financial market fluctuations," Nature, Nature, vol. 423(6937), pages 267-270, May.
    26. Saatcioglu, Kemal & Starks, Laura T., 1998. "The stock price-volume relationship in emerging stock markets: the case of Latin America," International Journal of Forecasting, Elsevier, vol. 14(2), pages 215-225, June.
    27. Zheng, B. & Ren, F. & Trimper, S. & Zheng, D.F., 2004. "A generalized dynamic herding model with feed-back interactions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 343(C), pages 653-661.
    28. F. Ren & B. Zheng & H. Lin & L. Y. Wen & S. Trimper, 2005. "Persistence Probabilities of the German DAX and Shanghai Index," Papers nlin/0511048, arXiv.org.
    29. Parameswaran Gopikrishnan & Vasiliki Plerou & Xavier Gabaix & H. Eugene Stanley, 2000. "Statistical Properties of Share Volume Traded in Financial Markets," Papers cond-mat/0008113, arXiv.org.
    30. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
    31. Qiu, T. & Zheng, B. & Ren, F. & Trimper, S., 2007. "Statistical properties of German Dax and Chinese indices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 378(2), pages 387-398.
    32. Gallant, A Ronald & Rossi, Peter E & Tauchen, George, 1992. "Stock Prices and Volume," The Review of Financial Studies, Society for Financial Studies, vol. 5(2), pages 199-242.
    33. Gao-Feng Gu & Wei-Xing Zhou, 2008. "Emergence of long memory in stock volatility from a modified Mike-Farmer model," Papers 0807.4639, arXiv.org, revised May 2009.
    34. Vasiliki Plerou & Parameswaran Gopikrishnan & Xavier Gabaix & H. Eugene Stanley, 2001. "Quantifying Stock Price Response to Demand Fluctuations," Papers cond-mat/0106657, arXiv.org.
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