Value-at-Risk (VaR) has emerged as the standard tool for measuring and reporting financial market risk. Currently, more than eighty commercial vendors offer enterprise or trading risk management systems which report VaR-like measures. Risk managers are therefore often left with the daunting task...

Value-at-Risk (VaR) and Expected Shortfall (ES) are increasingly used in portfolio risk measurement, risk capital allocation and performance attribution. Financial risk managers are therefore rightfully concerned with the precision of typical VaR and ES techniques. The purpose of this paper is...