Empirical Study on Fluctuation Theorem for Volatility Cascade Processes in Stock Markets

Area of Science:

• Financial market analysis
• Non-equilibrium thermodynamics
• Turbulence theory

Background:

• Financial markets exhibit intermittency in volatility, analogous to phenomena observed in developed turbulence.
• Turbulence intermittency is explained by energy cascades; similar cascade processes are proposed for financial time series.
• Understanding volatility cascades is crucial for characterizing financial market dynamics.

Purpose of the Study:

• To model and investigate volatility cascade processes in financial markets using stochastic thermodynamics.
• To apply thermodynamic concepts (temperature, heat, work, entropy) to financial market analysis.
• To empirically validate the model using stock market data from the London Stock Exchange (LSE) and Tokyo Stock Exchange (TSE).

Main Methods:

• Developed a Langevin system model to describe financial market dynamics and volatility cascades.
• Applied the framework of stochastic thermodynamics to analyze individual volatility cascade trajectories.
• Empirically analyzed intraday stock price data from the LSE and TSE using wavelet analysis.

Main Results:

• The Langevin-based model successfully reproduced the empirical distribution of volatility across time scales.
• Volatility cascade trajectories satisfied the Integral Fluctuation Theorem, indicating consistency with entropy production.
• LSE data showed causal volatility cascades (larger to smaller time scales), aligning with financial time series stylized facts.

Conclusions:

• The study demonstrates the utility of non-equilibrium thermodynamics in understanding financial market volatility.
• Empirical findings reveal distinct temporal behaviors of volatility cascades: causal for LSE, and mixed causal/anti-causal for TSE.
• The research highlights cross-market differences in volatility dynamics, suggesting varied underlying market mechanisms.