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Empirical Laws Of A Stock Price Index And A Stochastic Model

Author

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  • TAISEI KAIZOJI

    (Division of Social Sciences, International Christian University, 3-10-2 Osawa, Mitaka, Tokyo 181-8585, Japan;
    Econophysics Laboratory, 5-9-7-B Higashi-cho, Koganei-shi, Tokyo 184-0011, Japan)

  • MICHIYO KAIZOJI

    (Econophysics Laboratory, 5-9-7-B Higashi-cho, Koganei-shi, Tokyo 184-0011, Japan)

Abstract

Recent works by econo-physicists [5,8,15,19] have shown that the probability function of the share returns and the volatility satisfies a power law with an exponent close to 4. On the other hand, we investigated quantitatively the return and the volatility of the daily data of the Nikkei 225 index from 1990 to 2003, and we found that the distributions of the returns and the volatility can be accurately described by the exponential distributions [11]. We then propose a stochastic model of stock markets that can reproduce these empirical laws. In our model the fluctuations of stock prices are caused by interactions among traders. We indicate that the model can reproduce the empirical facts mentioned above. In particular, we show that the interaction strengths among traders are a key variable that can distinguish the emergence of the exponential distribution or the power-law distribution.

Suggested Citation

  • Taisei Kaizoji & Michiyo Kaizoji, 2003. "Empirical Laws Of A Stock Price Index And A Stochastic Model," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 6(03), pages 303-312.
    • Handle: RePEc:wsi:acsxxx:v:06:y:2003:i:03:n:s0219525903000906
    DOI: 10.1142/S0219525903000906
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    References listed on IDEAS

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    1. Kaizoji, Taisei, 2004. "Inflation and deflation in financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 343(C), pages 662-668.
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    Cited by:

    1. Pan, Raj Kumar & Sinha, Sitabhra, 2008. "Inverse-cubic law of index fluctuation distribution in Indian markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(8), pages 2055-2065.
    2. Taisei Kaizoji, 2013. "Modelling of Stock Returns and Trading Volume," IIM Kozhikode Society & Management Review, , vol. 2(2), pages 147-155, July.
    3. Taisei Kaizoji, 2010. "Stock volatility in the periods of booms and stagnations," EERI Research Paper Series EERI_RP_2010_07, Economics and Econometrics Research Institute (EERI), Brussels.
    4. Taisei Kaizoji, 2013. "Modeling of Stock Returns and Trading Volume," Papers 1309.2416, arXiv.org.
    5. Fabio Pizzutilo, 2013. "The Distribution of the Returns of Japanese Stocks and Portfolios," Asian Economic and Financial Review, Asian Economic and Social Society, vol. 3(9), pages 1249-1259, September.
    6. Bikramaditya Ghosh & Spyros Papathanasiou & Georgios Pergeris, 2022. "Did cryptocurrencies exhibit log‐periodic power law signature during the second wave of COVID‐19?," Economic Notes, Banca Monte dei Paschi di Siena SpA, vol. 51(3), November.
    7. Ramos, Antônio M.T. & Carvalho, J.A. & Vasconcelos, G.L., 2016. "Exponential model for option prices: Application to the Brazilian market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 445(C), pages 161-168.
    8. Taisei Kaizoji, 2005. "Comparison of volatility distributions in the periods of booms and stagnations: an empirical study on stock price indices," Papers physics/0506114, arXiv.org.

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