A joint quantile and expected shortfall regression framework

By Timo Dimitriadis, Sebastian Bayer. Electronic Journal of Statistics, 2017

60 citations recorded by the source corpus.

We introduce a novel regression framework which simultaneously models the quantile and the Expected Shortfall (ES) of a response variable given a set of covariates. This regression is based on a strictly consistent loss function for the pair quantile and ES, which allows for M- and Z-estimation of the joint regression parameters. We show consistency and asymptotic normality for both estimators under weak regularity conditions. The underlying loss function depends on two specification functions, whose choice affects the properties of the resulting estimators. We find that the Z-estimator is numerically unstable and thus, we rely on M-estimation of the model parameters. Extensive simulations verify the asymptotic properties and analyze the small sample behavior of the M-estimator for different specification functions. This joint regression framework allows for various applications including estimating, forecasting, and backtesting ES, which is particularly relevant in light of the recent introduction of ES into the Basel Accords.

Subfields: Finance, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/08b03c20c1e67607b687b446e8e563eb8ec2da61

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Citations in the corpus

Forecast combinations for value at risk and expected shortfall (2020, methodology): “(2019), who use the AL score to estimate dynamic models, and Dimitriadis and Bayer (2017), who present a regression framework for VaR and ES.”