title: Universality of market superstatistics.
abstract: We use a key concept of the continuous-time random walk formalism, i.e., continuous and fluctuating interevent times in which mutual dependence is taken into account, to model market fluctuation data when traders experience excessive (or superthreshold) losses or excessive (or superthreshold) profits. We analytically derive a class of "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 discrete (or step) time as a control variable to derive a universal description of empirical data collapse. Our dominant 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 itself and a "superscaling" configuration emerges. Thanks to the Weibull copula function, our approach reproduces the empirically proven dependence between successive interevent times. We also use the approach to calculate a dynamic risk function and hence the dynamic VaR, which is significant in financial risk analysis. 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. We also extend our original approach to cover empirical seismic activity data (e.g., given by Corral), the interevent times of which range from minutes to years. Superpositioned superstatistics is another class of superstatistics that protects power-law behavior both for short- and long-time behaviors. These behaviors describe well the collapse of seismic activity data and capture so-called volatility clustering phenomena.
authors.affiliation: Faculty of Physics, University of Warsaw, Pasteur 5, PL-02093 Warsaw, Poland.
authors.forename: Mateusz
authors.initials: M
authors.lastname: Denys
authors.affiliation: Faculty of Physics, University of Warsaw, Pasteur 5, PL-02093 Warsaw, Poland.
authors.forename: Tomasz
authors.initials: T
authors.lastname: Gubiec
authors.affiliation: Faculty of Physics, University of Warsaw, Pasteur 5, PL-02093 Warsaw, Poland.
authors.forename: Ryszard
authors.initials: R
authors.lastname: Kutner
authors.affiliation: Department of Management, Technology and Economics, ETHZ, Scheuchzerstrasse 7, CH-8092 Zürich, Switzerland; Faculty of Physics, University of Warsaw, Pasteur 5, PL-02093 Warsaw, Poland; and Center for Polymer Studies and Department of Physics, Boston University, Boston, Massachusetts 02215, USA.
authors.forename: Maciej
authors.initials: M
authors.lastname: Jagielski
authors.affiliation: Center for Polymer Studies and Department of Physics, Boston University, Boston, Massachusetts 02215, USA.
authors.forename: H Eugene
authors.initials: HE
authors.lastname: Stanley