Multiday expected shortfall under generalized t distributions : evidence from global stock market

We apply seven alternative t-distributions to estimate the market risk measures Value at Risk (VaR) and itsextension Expected Shortfall (ES). Of these seven, the twin t-distribution (TT) of Baker and Jackson (2014) andgeneralized asymmetric distribution (GAT) of Baker (2016) are applied for the first time to estimate market risk.We analytically estimate VaR and ES over one-day horizon and extend this to multi-day horizon using MonteCarlo simulation. We find that taken together TT and GAT distributions provide the best back-testing resultsacross individual confidence levels and horizons for majority of scenarios. Moreover, we find that with thelengthening of time horizon, TT and GAT models performs well, such that at the ten-day horizon, GAT providesthe best back-testing results for all of the five indices and the TT model provides the second best results,irrespective period of study and confidence level