Statistical Collapse of Excessive Market Losses
M. Denys a, M. Jagielskia,b,c, T. Gubiec a, R. Kutner a and H.E. Stanley b
aFaculty of Physics, University of Warsaw, L. Pasteura 5, PL-02-093 Warsaw, Poland
bCenter for Polymer Studies and Dept. of Physics, Boston Univ., Boston, MA 02215, USA
cDepartment of Management, Technology and Economics, ETHZ, Scheuchzerstr. 7, CH-8092 Z├╝rich, Switzerland
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We analytically derive superstatistics (or complex statistics) that accurately model empirical market activity data (supplied by Bogachev, Ludescher, Tsallis, and Bunde) exhibiting transition thresholds. We measure the interevent times between excessive losses (that is, greater than some threshold) and use the mean interevent time as a control variable to derive a universal description of empirical data collapse. Our superstatistic value is a power-law corrected by the lower incomplete gamma function, which asymptotically tends toward robustness but initially gives an exponential. We find that the scaling shape exponent that drives our superstatistics subordinates themselves and a "superscaling" configuration emerges.

DOI: 10.12693/APhysPolA.129.913
PACS numbers: 89.65 Gh, 05.40.-a, 89.75.Da