Kullback-Leibler cluster entropy to quantify volatility correlation and risk diversity

Area of Science:

• Quantitative Finance
• Statistical Modeling
• Time Series Analysis

Background:

• Stochastic volatility is crucial in financial markets.
• Existing entropy measures offer limited perspectives on volatility dynamics.
• Fractional stochastic processes model asset behavior effectively.

Purpose of the Study:

• To evaluate Kullback-Leibler cluster entropy for realized volatility.
• To compare Kullback-Leibler entropy with Shannon entropy for stochastic volatility.
• To develop and test a portfolio strategy based on Kullback-Leibler entropy.

Main Methods:

• Kullback-Leibler cluster entropy calculation for empirical and model distributions.
• Modeling realized volatility using time-dependent fractional stochastic processes.
• Constructing a multiperiod portfolio based on Kullback-Leibler entropy diversity indexes.

Main Results:

• Kullback-Leibler entropy provides complementary insights to Shannon entropy.
• The realized volatility exhibits power-law distributions with positive correlation.
• The Kullback-Leibler entropy-based portfolio shows superior robustness and performance.

Conclusions:

• Kullback-Leibler entropy offers a valuable tool for analyzing stochastic volatility.
• The proposed portfolio strategy enhances financial market performance.
• This approach provides a novel framework for portfolio optimization.