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Modeling of Stock Returns and Trading Volume

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  • Taisei Kaizoji

Abstract

In this study, we investigate the statistical properties of the returns and the trading volume. We show a typical example of power-law distributions of the return and of the trading volume. Next, we propose an interacting agent model of stock markets inspired from statistical mechanics [24] to explore the empirical findings. We show that as the interaction among the interacting traders strengthens both the returns and the trading volume present power-law behavior.

Suggested Citation

  • Taisei Kaizoji, 2013. "Modeling of Stock Returns and Trading Volume," Papers 1309.2416, arXiv.org.
  • Handle: RePEc:arx:papers:1309.2416
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    References listed on IDEAS

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    1. John Y. Campbell & Sanford J. Grossman & Jiang Wang, 1993. "Trading Volume and Serial Correlation in Stock Returns," The Quarterly Journal of Economics, Oxford University Press, vol. 108(4), pages 905-939.
    2. Burton G. Malkiel, 2003. "The Efficient Market Hypothesis and Its Critics," Working Papers 111, Princeton University, Department of Economics, Center for Economic Policy Studies..
    3. Epps, Thomas W, 1975. "Security Price Changes and Transaction Volumes: Theory and Evidence," American Economic Review, American Economic Association, vol. 65(4), pages 586-597, September.
    4. Lo, Andrew W & Wang, Jiang, 2000. "Trading Volume: Definitions, Data Analysis, and Implications of Portfolio Theory," Review of Financial Studies, Society for Financial Studies, vol. 13(2), pages 257-300.
    5. repec:pri:cepsud:91malkiel is not listed on IDEAS
    6. Kaizoji, Taisei & Bornholdt, Stefan & Fujiwara, Yoshi, 2002. "Dynamics of price and trading volume in a spin model of stock markets with heterogeneous agents," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 316(1), pages 441-452.
    7. Schwert, G William, 1989. " Why Does Stock Market Volatility Change over Time?," Journal of Finance, American Finance Association, vol. 44(5), pages 1115-1153, December.
    8. Kaizoji, Taisei, 2000. "Speculative bubbles and crashes in stock markets: an interacting-agent model of speculative activity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(3), pages 493-506.
    9. Jones, Charles M & Kaul, Gautam & Lipson, Marc L, 1994. "Transactions, Volume, and Volatility," Review of Financial Studies, Society for Financial Studies, vol. 7(4), pages 631-651.
    10. Burton G. Malkiel, 2003. "The Efficient Market Hypothesis and Its Critics," Journal of Economic Perspectives, American Economic Association, vol. 17(1), pages 59-82, Winter.
    11. Gallant, A Ronald & Rossi, Peter E & Tauchen, George, 1992. "Stock Prices and Volume," Review of Financial Studies, Society for Financial Studies, vol. 5(2), pages 199-242.
    12. Taisei Kaizoji & Masahide Nuki, 2003. "Scaling Law for the Distribution of Fluctuations of Share Volume," Papers cond-mat/0302468, arXiv.org, revised Mar 2006.
    13. Copeland, Thomas E, 1976. "A Model of Asset Trading under the Assumption of Sequential Information Arrival," Journal of Finance, American Finance Association, vol. 31(4), pages 1149-1168, September.
    14. 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(01), pages 109-126, March.
    15. Vasiliki Plerou & Parameswaran Gopikrishnan & Xavier Gabaix & H. Eugene Stanley, 2001. "Quantifying Stock Price Response to Demand Fluctuations," Papers cond-mat/0106657, arXiv.org.
    16. V. Plerou & P. Gopikrishnan & X. Gabaix & L. A. N. Amaral & H. E. Stanley, 2001. "Price fluctuations, market activity and trading volume," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 262-269.
    17. Kaizoji, Taisei, 2001. "A model of international financial crises," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 299(1), pages 279-293.
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