Abstrakt
We propose a generalized risk measure for expectile-based expected shortfall estimation. The generalization is designed with a mixture of Gaussian and Laplace densities.
Our plug-in estimator is derived from an analytic relationship between expectiles and expected shortfall. We investigate the sensitivity and robustness of the expected shortfall to the underlying mixture parameter specification and the risk level.
Empirical results from the US, German and UK stock markets and for selected NASDAQ blue chip companies indicate that expected shortfall can be successfully estimated using the proposed method on a monthly, weekly, daily and intra-day basis using a 1-year or 1-day time horizon across different risk levels.