Applying GARCH-EVT-Copula Models for Portfolio Value-at-Risk on G7 Currency Markets

This research estimates portfolio VaR (Value-at-Risk) on G7 exchange rates using a GJR-GARCH-EVT (extreme value theory)-Copula based approach. We first extracts the filtered residuals from each return series via an asymmetric GJR-GARCH model, then constructs the semi-parametric empirical marginal cumulative distribution function (CDF) of each asset using a Gaussian kernel estimate for the interior and a generalized Pareto distribution (GPD) estimate for the upper and lower tails (our approach focuses on the entire distribution rather than the tail distribution only). A Student's t copula is then fit to the data and used to induce correlation between the simulated residuals of each asset. In order to test the effectiveness of this model we backtest the estimated VaRs over a time window of 200 days. Empirical results demonstrate that our GJR-GARCH-EVT-Copula based approach outperforms traditional methods such as historical simulation or conditional Gaussian model.