Portfolio Risk Management using Extreme Value Theory and Vine Copulas

We estimate the one- and ten-day-ahead Value-at-Risk and the Expected Shortfall of a portfolio by using marginal modeling and two different dependence models. The marginal modeling consists of two steps. Firstly the returns are filtered by an asymmetric Markov-Switching ARMA-GARCH model (ARMA-MS-GARCH-GJR) and secondly the tails of the filtered returns are estimated by the Generalized Pareto Distribution. We fit two different joint distributions on these transformed returns: Vine Copulas and a distribution based on Multivariate Extreme Value Theory (MEVT). These two models will be compared with the t copula by backtesting the Value-at-Risk (VaR) and Expected Shortfall (ES) in two periods: during the Financial Crisis in 2008 and during a stable period. We show from the backtesting that all joint distributions are capable of providing accurate one-day-ahead VaR and ES forecasts, while the ten-day-ahead forecasts during the Financial Crisis are not accurate. It follows that during periods of financial distress the models with fatter tails are in favor, such as the t copula and the Vine Copula, while in stable periods these models tend to overestimate the Value-at-Risk and the Expected Shortfall slightly. In stable periods the model based on MEVT is preferred.