Scaling of the distribution of fluctuations of financial market indices.
Parameswaran Gopikrishnan,Vasiliki Plerou,Vasiliki Plerou,Luís A. Nunes Amaral,Martin Meyer,H. Eugene Stanley +5 more
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Estimates of alpha consistent with those describing the distribution of S&P 500 daily returns are found, and for time scales longer than (deltat)x approximately 4 d, the results are consistent with a slow convergence to Gaussian behavior.Abstract:
We study the distribution of fluctuations of the S&P 500 index over a time scale deltat by analyzing three distinct databases. Database (i) contains approximately 1 200 000 records, sampled at 1-min intervals, for the 13-year period 1984-1996, database (ii) contains 8686 daily records for the 35-year period 1962-1996, and database (iii) contains 852 monthly records for the 71-year period 1926-1996. We compute the probability distributions of returns over a time scale deltat, where deltat varies approximately over a factor of 10(4)-from 1 min up to more than one month. We find that the distributions for deltat<or= 4 d (1560 min) are consistent with a power-law asymptotic behavior, characterized by an exponent alpha approximately 3, well outside the stable Levy regime 0<alpha<2. To test the robustness of the S&P result, we perform a parallel analysis on two other financial market indices. Database (iv) contains 3560 daily records of the NIKKEI index for the 14-year period 1984-1997, and database (v) contains 4649 daily records of the Hang-Seng index for the 18-year period 1980-1997. We find estimates of alpha consistent with those describing the distribution of S&P 500 daily returns. One possible reason for the scaling of these distributions is the long persistence of the autocorrelation function of the volatility. For time scales longer than (deltat)x approximately 4 d, our results are consistent with a slow convergence to Gaussian behavior.read more
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References
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The econometrics of financial markets
TL;DR: In this paper, Campbell, Lo, and MacKinlay present an attempt by three well-known and well-respected scholars to fill an acknowledged void in the empirical finance literature, a text covering the burgeoning field of empirical finance.
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Introduction to Econophysics: Correlations and Complexity in Finance
TL;DR: Economists and workers in the financial world will find useful the presentation of empirical analysis methods and well-formulated theoretical tools that might help describe systems composed of a huge number of interacting subsystems.