Universality of market superstatistics

Area of Science:

• Quantitative Finance
• Statistical Physics
• Complex Systems Analysis

Background:

• Market fluctuations exhibit complex dynamics, particularly during periods of extreme trader gains or losses.
• Existing models often struggle to capture the interdependencies and thresholds observed in empirical financial and seismic data.

Purpose of the Study:

• To develop a robust statistical framework, termed "superstatistics," for modeling market and seismic activity.
• To analytically derive and validate a universal description of empirical data collapse using interevent times.
• To introduce a dynamic risk assessment tool, including dynamic Value at Risk (VaR), for financial applications.

Main Methods:

• Utilizing the continuous-time random walk formalism to model fluctuating interevent times.
• Analytically deriving a class of superstatistics, incorporating power-law and incomplete gamma functions.
• Employing the Weibull copula function to reproduce the dependence between successive interevent times.
• Extending the superstatistics approach to analyze seismic activity data.

Main Results:

• A novel superstatistics model accurately captures empirical market data with transition thresholds.
• A universal data collapse is achieved using mean interevent time as a control variable.
• The derived superstatistics exhibit robustness, transitioning from exponential to power-law behavior.
• A functional balance between excessive profits and losses is demonstrated, explainable by superstatistics.
• The model successfully reproduces seismic activity data, including volatility clustering.

Conclusions:

• Superstatistics provide a unifying framework for understanding complex phenomena in financial markets and seismology.
• The approach offers a powerful tool for dynamic risk assessment and analysis of interevent time dependencies.
• The findings highlight the applicability of continuous-time random walk formalisms beyond traditional financial modeling.