Paper: arXiv 2504.18958

Authors: Masoud Ataei

Abstract

This paper investigates the structural dynamics of stock market volatility through the Financial Chaos Index, a tensor- and eigenvalue-based measure designed to capture realized volatility via mutual fluctuations among asset prices. Motivated by empirical evidence of regime-dependent volatility behavior and perceptual time dilation during financial crises, we develop a regime-switching framework based on the Modified Lognormal Power-Law distribution. Analysis of the FCIX from January 1990 to December 2023 identifies three distinct market regimes, low-chaos, intermediate-chaos, and high-chaos, each characterized by differing levels of systemic stress, statistical dispersion and persistence characteristics. Building upon the segmented regime structure, we further examine the informational forces that shape forward-looking market expectations. Using sentiment-based predictors derived from the Equity Market Volatility tracker, we employ an elastic net regression model to forecast implied volatility, as proxied by the VIX index. Our findings indicate that shifts in macroeconomic, financial, policy, and geopolitical uncertainty exhibit strong predictive power for volatility dynamics across regimes. Together, these results offer a unified empirical perspective on how systemic uncertainty governs both the realized evolution of financial markets and the anticipatory behavior embedded in implied volatility measures.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 7.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper employs advanced mathematical concepts including tensor analysis, eigenvalue decompositions, and the Modified Lognormal Power-Law distribution for regime switching. It demonstrates high empirical rigor through the use of real-world data (S&P 500 assets over 33 years), backtest-ready forecasting models (elastic net regression for VIX prediction), and statistical validation of regimes.

Research Flowchart

  flowchart TD
  A["Research Goal<br>Model Volatility Structure & Drivers"] --> B["Data & Inputs<br>FCIX, EMV Tracker, VIX 1990-2023"]
  B --> C["Computational Process<br>Regime-Switching Framework"]
  C --> D{"Regime Identification<br>Modified Lognormal Power-Law"}
  D --> E["Outcome 1: Three Market Regimes<br>Low/Intermediate/High Chaos"]
  D --> F["Computational Process<br>Elastic Net Regression"]
  F --> G["Outcome 2: Volatility Forecasting<br>Macro/Financial/Policy/Geopolitical Drivers"]
  E --> H["Unified Perspective<br>Systemic Uncertainty drives Realized & Implied Volatility"]
  G --> H

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