Estimating Value at Risk and Expected Shortfall Using Expectiles

Expectile models are derived using asymmetric least squares. A simple formula relates the expectile to the expectation of exceedances beyond the expectile. We use this as the basis for estimating expected shortfall. It has been proposed that the quantile be estimated by the expectile for which the proportion of observations below the expectile is ?. In this way, an expectile can be used to estimate value at risk. Using expectiles has the appeal of avoiding distributional assumptions. For univariate modelling, we introduce conditional autoregressive expectiles (CARE). Empirical results for the new approach are competitive with established benchmarks methods.