Universality of market superstatistics |
Mateusz Denys ^{1}, Maciej Jagielski ^{1,2}, Tomasz Gubiec ^{1}, Ryszard Kutner ^{1}, Eugene Stanley ^{2} |
1. Uniwersytet Warszawski, Wydział Fizyki, ul. Pasteura 5, Warszawa 02-093, Poland |
Abstract |
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 interevent times between excessive losses and excessive profits, and use the mean interevent 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 incomplete gamma function, which tends toward the power-law only during short interevent 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. |