Hedging for the Regime-Switching Price Model Based on Non-Extensive Statistical Mechanics

Area of Science:

• Quantitative Finance
• Statistical Mechanics
• Stochastic Processes

Background:

• Accurate asset price modeling is crucial for financial risk management.
• Traditional models often fail to capture empirical features like fat tails and regime switching.
• Understanding macroeconomic influences on asset prices is essential for robust financial strategies.

Purpose of the Study:

• To develop a comprehensive asset price model incorporating non-extensive statistical mechanics and semi-Markov processes.
• To analyze and represent the peak and fat tail characteristics of asset returns.
• To address the hedging problem for contingent claims using risk-minimizing methods.

Main Methods:

• Application of non-extensive statistical mechanics principles.
• Integration of the semi-Markov process for modeling dynamic systems.
• Utilizing risk-minimizing techniques for optimal hedging strategy derivation.

Main Results:

• A novel asset price model capable of depicting fat tails and peak characteristics of returns.
• The model successfully captures the regime-switching phenomenon in macroeconomic systems.
• Explicit solutions for optimal hedging strategies for contingent claims were obtained.

Conclusions:

• The proposed model offers a more accurate description of asset price dynamics compared to traditional approaches.
• The integration of advanced statistical and stochastic methods enhances financial modeling capabilities.
• The derived hedging strategies provide practical tools for risk management in complex financial markets.