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Expected Shortfall (ES) is the average return on a risky asset conditional onthe return being below some quantile of its distribution, namely itsValue-at-Risk (VaR). The Basel III Accord, which will be implemented in theyears leading up to 2019, places new attention on ES, but unlike VaR, there islittle existing work on modeling ES. We use recent results from statisticaldecision theory to overcome the problem of "elicitability" for ES by jointlymodelling ES and VaR, and propose new dynamic models for these risk measures.We provide estimation and inference methods for the proposed models, andconfirm via simulation studies that the methods have good finite-sampleproperties. We apply these models to daily returns on four international equityindices, and find the proposed new ES-VaR models outperform forecasts based onGARCH or rolling window models.

Dynamic Semiparametric Models for Expected Shortfall (and Value-at-Risk)