Universality of market superstatistics

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 powerlaw corrected by the lower incomplete gamma function, which asymptotically tends toward robustness but initially gives an exponential, and (ii) a powerlaw 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.

References in corpus (8)

• A Random Walk to a Non-Ergodic Equilibrium Concept
• A model for interevent times with long tails and multifractality in human communications: An application to financial trading
• Stochastic model of financial markets reproducing scaling and memory in volatility return intervals
• Inter-occurrence times and universal laws in finance, earthquakes and genomes
• Fluctuations around equilibrium laws in ergodic continuous-time random walks
• Interplay between endogenous and exogenous fluctuations in financial markets
• Aftershock prediction for high-frequency financial markets' dynamics
• Universality of Tsallis q-exponential of interoccurrence times within the microscopic model of cunning agents

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