Risk Estimation With Composite Quantile Regression

New methods for the estimation of the popular risk measures expected shortfall (ES) and Value-at-Risk (VaR) are introduced. These are based on a novel variant of composite quantile regression (CQR), which allows for the simultaneous estimation of quantiles at several levels at once. An extensive simulation study is performed, along with a data analysis based on two major US market indices and two financial sector stocks. The results suggest that the method has a good finite sample performance. This is the first methodology to use CQR for risk estimation.