The use of the tail dependence function for high quantile risk measure analysis: an application to portfolio optimization

Adequate risk modelling in a financial portfolio has become the central part of its analysis. To this end, risk measures have proven to be very effective. However, the efficiency of these measures lies in the accurate modelling of both the individual behaviour as well as the dependence between the assets. In particular, tail dependence has become crucial in analysing Value at Risk (VaR) and the Expected Shortfall (ES) in high quantiles. This study introduces a new methodology to estimate high quantile risk measures based on the Tail Dependence Function. With this function, we can estimate asset dependence by focusing on replicating the extreme behaviour. In an empirical study, we estimate the VaR and ES of a portfolio of stock indices during the current pandemic considering our approach along with the most traditional GARCH-Copula and historical approaches as benchmark estimators. Our approach yields superior estimators with respect to the benchmark estimators in high quantiles.