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Modeling Regime Structure and Informational Drivers of Stock Market Volatility via the Financial Chaos Index

Masoud Ataei

TL;DR

The paper addresses the nonstationary, regime-dependent nature of stock market volatility by introducing the Financial Chaos Index (FCIX), a tensor-based measure that captures higher-order interdependencies among asset prices. It combines a nonparametric, kernel-based regime segmentation with a finite mixture of the Modified Lognormal Power-Law (MLP) distribution to identify three volatility regimes (low-chaos, intermediate-chaos, high-chaos) over 1990–2023, and links realized volatility dynamics to forward-looking behavior through EMV-driven elastic-net forecasts of the VIX. The study shows regime-specific drivers of implied volatility, highlighting how macroeconomic, policy, and geopolitical uncertainty influence market expectations differently across regimes. Together, the results offer a unified framework for understanding systemic risk, regime detection, and regime-aware volatility forecasting with practical implications for risk management and macroprudential policy.

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.

Modeling Regime Structure and Informational Drivers of Stock Market Volatility via the Financial Chaos Index

TL;DR

The paper addresses the nonstationary, regime-dependent nature of stock market volatility by introducing the Financial Chaos Index (FCIX), a tensor-based measure that captures higher-order interdependencies among asset prices. It combines a nonparametric, kernel-based regime segmentation with a finite mixture of the Modified Lognormal Power-Law (MLP) distribution to identify three volatility regimes (low-chaos, intermediate-chaos, high-chaos) over 1990–2023, and links realized volatility dynamics to forward-looking behavior through EMV-driven elastic-net forecasts of the VIX. The study shows regime-specific drivers of implied volatility, highlighting how macroeconomic, policy, and geopolitical uncertainty influence market expectations differently across regimes. Together, the results offer a unified framework for understanding systemic risk, regime detection, and regime-aware volatility forecasting with practical implications for risk management and macroprudential policy.

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.
Paper Structure (6 sections, 30 equations, 5 figures, 4 tables)

This paper contains 6 sections, 30 equations, 5 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Financial Chaos Index
  4. Regime Analysis
  5. Forces Driving Market Volatility
  6. Conclusion

Figures (5)

  • Figure 1: Schematic illustration of a reciprocal pairwise comparison tensor (RPCT) ataei2021theory.
  • Figure 2: Monthly $\mathrm{FCIX}$ during January $1990$-December $2023$.
  • Figure 3: Stock market segmentation during January $1990$-December $2023$.
  • Figure 4: Frequency histogram for $\mathrm{FCIX}$ during January $1990$-December $2023$.
  • Figure 5: Plots of the probability density functions of market regimes.