A new non-parametric estimation of the expected shortfall for dependent financial losses

In this paper, we address the problem of kernel estimation of the Expected Shortfall (ES) risk measure for financial losses that satisfy the α-mixing conditions. First, we introduce a new non-parametric estimator for the ES measure using a kernel estimation. Given that the ES measure is the sum of the Value-at-Risk and the mean-excess function, we provide an estimation of the ES as a sum of the estimators of these two components. Our new estimator has a closed-form expression that depends on the choice of the kernel smoothing function, and we derive these expressions in the case of Gaussian, Uniform, and Epanechnikov kernel functions. We study the asymptotic properties of this new estimator and compare it to the Scaillet estimator. Capitalizing on the properties of these two estimators, we combine them to create a new estimator for the ES which reduces the bias and lowers the mean square error. The combined estimator shows better stability with respect to the choice of the kernel smoothing parameter. Our findings are illustrated through some numerical examples that help us to assess the small sample properties of the different estimators considered in this paper. •Introduction of the mean-excess-based (MEB) estimator for the expected shortfall (ES) risk measure.•Derivation of the asymptotic properties of this new MEB estimator.•Comparison of the performance of the MEB estimator and Scaillet’s estimator.•Introduction of a bias-reduced estimator for the ES, which is defined as a combination of the MEB estimator and Scaillet’s estimator.