Value at Risk long memory volatility models with heavy-tailed distributions for cryptocurrencies.

Area of Science:

• Quantitative Finance
• Financial Econometrics
• Digital Asset Markets

Background:

• Cryptocurrency markets exhibit overlooked long-range dependence.
• High volatility and heavy tails are characteristic of digital asset returns.
• Accurate modeling of these features is crucial for risk management.

Purpose of the Study:

• Investigate volatility dynamics and long memory in major cryptocurrencies.
• Compare advanced long-memory volatility models against standard benchmarks.
• Enhance Value-at-Risk (VaR) estimation and volatility forecasting accuracy.

Main Methods:

• Employed long-memory extensions of GAS (Long memory GAS) and GARCH (Fractionally Integrated Asymmetric Power ARCH) models.
• Integrated heavy-tailed innovation distributions: Generalized Hyperbolic Distribution (GHD) and Generalized Lambda Distribution (GLD).
• Assessed model performance using VaR estimation, backtesting, and volatility forecasting metrics.

Main Results:

• Long memory models, especially FIAPARCH, consistently outperformed standard GAS and GARCH models.
• FIAPARCH demonstrated superior performance in capturing tail risk and volatility persistence.
• Evidence supports the critical role of long memory in modeling cryptocurrency risk.

Conclusions:

• Accounting for volatility persistence significantly enhances the accuracy of cryptocurrency risk estimates.
• Advanced long-memory models are essential for robust risk management in digital asset markets.
• Findings underscore the importance of incorporating long memory features for reliable financial forecasting.