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Comparison of volatility distributions in the periods of booms and stagnations: an empirical study on stock price indices

  • Taisei Kaizoji

The aim of this paper is to compare statistical properties of stock price indices in periods of booms with those in periods of stagnations. We use the daily data of the four stock price indices in the major stock markets in the world: (i) the Nikkei 225 index (Nikkei 225) from January 4, 1975 to August 18, 2004, of (ii) the Dow Jones Industrial Average (DJIA) from January 2, 1946 to August 18, 2004, of (iii) Standard and Poor's 500 index (SP500) from November 22, 1982 to August 18, 2004, and of (iii) the Financial Times Stock Exchange 100 index (FT 100) from April 2, 1984 to August 18, 2004. We divide the time series of each of these indices in the two periods: booms and stagnations, and investigate the statistical properties of absolute log returns, which is a typical measure of volatility, for each period. We find that (i) the tail of the distribution of the absolute log-returns is approximated by a power-law function with the exponent close to 3 in the periods of booms while the distribution is described by an exponential function with the scale parameter close to unity in the periods of stagnations.

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Paper provided by in its series Papers with number physics/0506114.

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Date of creation: Jun 2005
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Handle: RePEc:arx:papers:physics/0506114
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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.
  2. Michel M. Dacorogna, & Ulrich A. Muller & Olivier V. Pictet & Casper De Vries,, . "The Distribution of Extremal Foreign Exchange Rate Returns in Extremely Large Data Sets," Working Papers 1992-10-22, Olsen and Associates.
  3. 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.
  4. Pagan, Adrian, 1996. "The econometrics of financial markets," Journal of Empirical Finance, Elsevier, vol. 3(1), pages 15-102, May.
  5. P. Gopikrishnan & M. Meyer & L.A.N. Amaral & H.E. Stanley, 1998. "Inverse cubic law for the distribution of stock price variations," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, vol. 3(2), pages 139-140, July.
  6. Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, vol. 36, pages 394.
  7. Richard B. Olsen & Ulrich A. Müller & Michel M. Dacorogna & Olivier V. Pictet & Rakhal R. Davé & Dominique M. Guillaume, 1997. "From the bird's eye to the microscope: A survey of new stylized facts of the intra-daily foreign exchange markets (*)," Finance and Stochastics, Springer, vol. 1(2), pages 95-129.
  8. Longin, Francois M, 1996. "The Asymptotic Distribution of Extreme Stock Market Returns," The Journal of Business, University of Chicago Press, vol. 69(3), pages 383-408, July.
  9. Parameswaran Gopikrishnan & Vasiliki Plerou & Luis A. Nunes Amaral & Martin Meyer & H. Eugene Stanley, 1999. "Scaling of the distribution of fluctuations of financial market indices," Papers cond-mat/9905305,
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