A Varying-Coefficient Expectile Model for Estimating Value at Risk

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.

Previous studies on conditional EVaR estimation only considered parametric autoregressive model set-ups, which account for the stochastic dynamics of asset returns but ignore other exogenous economic and investment related factors. Our approach overcomes this drawback and allows expectiles to be modeled directly using covariates that may be exogenous or lagged dependent in a flexible way. Risk factors associated with profits and losses can then be identified via the expectile regression at different levels of prudentiality.