Statistical Physics Approaches to Financial Market Volatility: Power Laws, Multifractal Scaling, and Agent-Based Models of High-Frequency Trading Dynamics

Abstract

The application of statistical physics methods to financial markets, known as econophysics, has produced substantial empirical and theoretical insights over the past three decades. This paper presents a comprehensive empirical analysis of U.S. equity market volatility using statistical physics tools, including power-law tail analysis, multifractal scaling, and agent-based simulation of high-frequency trading dynamics. Empirical analysis draws on tick-level data from NYSE, NASDAQ, and CBOE covering 2005-2024, encompassing approximately 3.2 trillion trade observations across S&P 500 constituents. Power-law analysis of return distribution tails reveals empirical exponents consistent with the widely-reported inverse cubic law (α ≈ 3.0) for large stocks, with substantial cross-sectional variation and time evolution during high-volatility episodes. Multifractal detrended fluctuation analysis identifies significant multifractality in intraday returns and volume, with singularity spectra reflecting the interaction of multiple trading time scales. Agent-based simulations calibrated to empirical stylized facts reproduce key features of realized volatility, order flow autocorrelation, and cross-asset correlation dynamics. The paper contributes empirical evidence characterizing the scaling properties of contemporary electronic markets, theoretical insights from agent-based modelling, and bridges between statistical physics and financial economics literatures.