Single-Index Expectile Models for Estimating Conditional Value at Risk and Expected Shortfall

This article develops a single-index approach for modeling the expectile-based value at risk (EVaR). EVaR has an advantage over the conventional quantile-based VaR (QVaR) of being more sensitive to the magnitude of extreme losses. EVaR can also be used for calculating QVaR and expected shortfall (ES) by exploiting the one-to-one mapping from expectiles to quantiles and the relationship between VaR and ES. We develop an asymmetric least squares technique for estimating the unknown regression parameter and link function in a single-index model, and establish the asymptotic normality of the resultant estimators. Simulation studies and real data applications are conducted to illustrate the finite sample performance of the proposed methods.