Assessment of dependent risk using extreme value theory in a time-varying framework

Several extreme events in history have shown that the low probability and high impact extreme values may result in catastrophic losses. In this paper, we propose the use of extreme value theory with a time-varying framework to model the bivariate dependent insurance occurrences and provide more reliable risk measures, such as value at risk and expected shortfall. In this paper three models are considered; time series for the underlying volatility of the data, extreme value theory for the tail estimation, and copula to model the dependence structure are combined. The performance of the proposed generalized Pareto-GARCH-Copula model is tested using the violation numbers and backtesting methods. We then aim to assess the combined model in terms of its effectiveness in reducing the ruin probability. Results show that, compared to well-known traditional methods, which may underestimate the extreme risks, the dynamic generalized Pareto-GARCH-Copula model captures better the real-life data's behavior and results in lower ruin probabilities for heavy-tailed and non-conventional dependent insurance data.