Dynamic EVT–Copula models with endogenous linkage between extreme losses and dependence structure

This paper proposes a novel dynamic extreme value theory (EVT)–Copula modelling framework with endogenous linkage to model systemic risk arising from extreme losses and evolving dependence structures. The marginal distributions of asset losses are modelled using a peak-over-threshold approach. Then, exceedances follow generalized Pareto distributions with time-varying parameters and adaptive thresholds to capture non-stationary tail behavior. The dependence structure is specified through copula modelling of non-linear and asymmetric tail dependence across multiple financial entities. The endogenizing of the dependence copula parameters evolves according to score-driven mechanism augmented by extreme loss feedback. Specifically, the dependence parameter is modelled as a function of past dependence, score information, and aggregated magnitudes. Its captures the co-evaluation between marginal extremes and systemic independence. The estimation is carried out using inference functions for margins and canonical maximum likelihood for copula parameters exposed the computational tractability and efficiency. The proposed modelling enables the computation of systemic risk measures including value at risk, expected shortfall, conditional value at risk, marginal expected shortfall, and tail dependence coefficients. The empirical and simulation analyses demonstrate that the model effectively captures contagion effects and dynamic tail risk. The model provides a robust tool for actuarial risk management and financial stability assessment under extreme conditions.