Endogenous Crashes as Phase Transitions

This paper explores the mechanisms behind extreme financial events, specifically market crashes, by employing the theoretical framework of phase transitions. We focus on endogenous crashes, driven by internal market dynamics, and model these events as first-order phase transitions critical, stochastic, and dynamic. Through a comparative analysis of early warning signals associated with each type of transition, we demonstrate that dynamic phase transitions (DPT) offer a more accurate representation of market crashes than critical (CPT) or stochastic phase transitions (SPT). Unlike existing models, such as the Log-Periodic Power Law (LPPL) model, which often suffers from overfitting and false positives, our approach grounded in DPT provides a more robust prediction framework. Empirical findings, based on an analysis of S&P 500 stocks from 2019 to 2024, reveal significant trends in volatility and anomalous dimensions before crashes, supporting the superiority of the DPT model. This work contributes to a deeper understanding of the predictive signals preceding market crashes and offers a novel perspective on their underlying dynamics.