Integrated Econometric Framework for Forecasting Insurance Capital Requirements under Volatility Clustering and Tail Risk Using ARMA–GARCH, EVT-Enhanced GARCH, and DCC Dependence Modeling Approaches
Keywords:
Insurer capital requirements, ARMA-GARCH, Extreme Value Theory, DCC-GARCHAbstract
This study proposes an integrated econometric framework for forecasting insurer capital requirements under conditions of volatility clustering, heavy-tailed risk, and dynamic cross-market dependence. The framework combines ARMA-based mean modeling, GARCH-family volatility estimation, Extreme Value Theory (EVT) for tail risk refinement, and Dynamic Conditional Correlation (DCC) models for multivariate dependence structures. The motivation stems from the increasing instability of financial and insurance markets, where traditional risk models often underestimate extreme losses and correlation shifts during crises. Building on established literature in volatility modeling (Bollerslev, 1986; Engle, 2002) and tail risk estimation (McNeil & Frey, 2000; Gençay & Selçuk, 2004), the study integrates copula-inspired risk aggregation concepts and EVT-enhanced GARCH structures to improve capital forecasting accuracy. A conceptual empirical simulation is developed to illustrate insurer capital exposure under different market regimes. The findings suggest that EVT-enhanced GARCH significantly improves tail sensitivity, while DCC structures capture systemic risk spillovers more effectively than univariate models. The proposed framework provides a unified tool for regulators and insurers to estimate capital adequacy under Basel-aligned risk conditions and extreme market stress scenarios.
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