Regime-Switching Flexible (Quasi) Score-Driven Models: Analyzing and Forecasting Portfolio Risks through Value at Risk and Expected Shortfall

This paper addresses volatility modeling in financial markets with a focus on portfolios comprising stocks, cryptocurrencies, and mixed assets, underscoring the essential role of precise volatility forecasting for asset pricing, risk management, and macroeconomic policy design. We employ and critically compare advanced volatility models such as GARCH, GAS, and Quasi Score Driven (QSD) within a regime-switching framework, paired with various flexible parametric distributions. The study emphasizes the superiority of regime-switching models in predicting Value-at-Risk and Expected Shortfall, attributing this to their enhanced flexibility in capturing complex market dynamics and stylized facts. This comprehensive analysis incorporates 124 regime and non-regime switching models, including the GARCH, GAS, and QSD models, and their regime-switching variants such as MS-GARCH, MS-GAS, and MS-QSD. The evaluation focuses on their performance in VaR and ES backtests, conducted at both 95% and 99% confidence levels, supported by Model Confidence Set (MCS) assessments to filter out the most proficient models. By evaluating the models’ fit with empirical data and their reliability in risk measure forecasting, our findings offer significant insights into volatility dynamics, contributing to a deeper understanding and facilitating more effective financial decision making. A key observation is that models utilizing flexible distributions, i.e. distributions with at least one additional shape parameter, such as the Generalized Error Distribution (1), Skewed Student’s t (2), and Exponential Generalized Beta distribution of the second kind (2) demonstrate a significant advantage in accurately capturing the complexities of financial data, including fat tails and skewness, over simpler distributions. Furthermore, incorporating a regime-switching framework generally leads to more sophisticated VaR and ES predictions, however, results could be inconsistent due to the dependency on sample sizes, which is the case in cryptocurrency and mixed asset portfolios. Furthermore, the MCS analysis corroborates the dominance of regimeswitching models, particularly at higher confidence levels.

Keywords: Cryptocurrencies, Expected Shortfall, Financial Markets, Flexible Parametric Distributions, GARCH, GAS, Markov-Regime-Switching, Mixed Assets, QSD, Risk Management, Stock Portfolios, Value-at-Risk, Volatility Modeling.