Universality of market superstatistics. Superscaling

Mateusz Denys 1Maciej Jagielski 1,2Tomasz Gubiec 1Ryszard Kutner 1Eugene Stanley 2

1. Uniwersytet Warszawski, Wydział Fizyki, ul. Pasteura 5, Warszawa 02-093, Poland
2. Center for Polymer Studies and Department of Physics, Boston University, 590 Commonwealth Ave, Boston, MA 02215, United States


We use a continuous-time random walk (CTRW) to model market fluctuation data from times when traders experience excessive losses or excessive profits. We analytically derive “superstatistics” that accurately model empirical market activity data (supplied by Bogachev, Ludescher, Tsallis, and Bunde) that exhibit transition thresholds. We measure the inter-event times between excessive losses and excessive profits, and use the mean inter-event time as a control variable to derive a universal description of empirical data collapse. Our superstatistic value is a weighted sum of two components, (i) a power-law corrected by the lower incomplete gamma function, which asymptotically tends toward robustness but initially gives an exponential, and (ii) a power-law damped by the upper gamma function, which tends toward the power-law only during short inter-event times. We find that the scaling shape exponents that drive both components subordinate themselves and a “superscaling” configuration emerges. We use superstatistics to describe the hierarchical activity when component (i) reproduces the negative feedback and component (ii) reproduces the stylized fact of volatility clustering. Our results indicate that there is a functional (but not literal) balance between excessive profits and excessive losses that can be described using the same body of superstatistics, but different calibration values and driving parameters.


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Presentation: Invited oral at 8 Ogólnopolskie Sympozjum "Fizyka w Ekonomii i Naukach Społecznych", by Ryszard Kutner
See On-line Journal of 8 Ogólnopolskie Sympozjum "Fizyka w Ekonomii i Naukach Społecznych"

Submitted: 2015-05-04 15:43
Revised:   2015-11-07 15:13