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This study introduces entropy and Gaussian mixture models to better assess financial market volatility and risk. This approach offers a more robust evaluation than traditional methods assuming normal distributions for log-returns.

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Area of Science:

  • Quantitative Finance
  • Financial Risk Management
  • Statistical Modeling

Background:

  • Financial market volatility, the fluctuation of asset prices, is crucial for risk management.
  • Traditional volatility assessment often uses standard deviation of log-returns, assuming a Gaussian distribution.
  • This Gaussian assumption is frequently invalid for financial log-returns, limiting accuracy.

Purpose of the Study:

  • To explore the application of (differential) entropy for evaluating financial log-return volatility.
  • To develop a more accurate and robust framework for financial risk assessment.
  • To integrate advanced statistical methods for improved volatility and risk measure computation.

Main Methods:

  • Utilizing (differential) entropy to quantify financial log-return volatility.
  • Employing Gaussian mixture models to estimate the probability density of log-returns.
  • Applying the developed framework to compute risk measures like Value at Risk and Expected Shortfall.

Main Results:

  • The proposed entropy-based method provides an alternative to standard deviation for volatility assessment.
  • Gaussian mixture models effectively approximate non-Gaussian log-return distributions.
  • The integrated approach enhances the accuracy of financial risk measures.

Conclusions:

  • Entropy, combined with Gaussian mixture models, offers a superior framework for analyzing financial volatility.
  • This methodology addresses limitations of traditional approaches by not assuming Gaussian distributions.
  • The study provides a more robust foundation for financial risk management and decision-making.