A fractal-based approach for modeling stock price variations

Area of Science:

• Quantitative Finance
• Mathematical Modeling
• Financial Econometrics

Background:

• The global financial crisis highlighted vulnerabilities in financial systems and stock markets.
• Extreme price swings necessitate improved mathematical models for financial time series.
• Traditional financial modeling approaches struggle with market volatility and extreme events.

Purpose of the Study:

• To propose a novel fractal-based approach for modeling stock prices.
• To introduce the Multifractional Process with Random Exponent for financial time series analysis.
• To empirically validate the proposed model's effectiveness in capturing market dynamics.

Main Methods:

• Fractal-based modeling using a Multifractional Process with Random Exponent.
• Application to real-world stock market price data.
• Comparative analysis of model fit against traditional methods using three major stock indexes.

Main Results:

• The proposed fractal-based model demonstrates superior goodness of fit for actual stock price series.
• The Multifractional Process with Random Exponent effectively captures the complex dynamics of stock markets.
• Empirical evidence supports the model's ability to handle market volatility and extreme events.

Conclusions:

• Fractal-based modeling offers a more robust framework for understanding stock market behavior.
• The Multifractional Process with Random Exponent is a promising tool for financial econometrics.
• This approach provides a better alternative for modeling financial markets, particularly during crises.