Weighted Nadaraya-Watson Estimation of Conditional Expected Shortfall

Abstract

This paper addresses the problem of nonparametric estimation of the conditional expected shortfall (CES) that has gained popularity in financial risk management. We propose a new nonparametric estimator of the CES. The proposed estimator is defined as a conditional counterpart of the sample average estimator of the unconditional expected shortfall, where the empirical distribution function is replaced by the weighted Nadaraya–Watson estimator of the conditional distribution function. We establish asymptotic normality of the proposed estimator under an α-mixing condition. The asymptotic results reveal that the proposed estimator has a good bias property. Simulation results illustrate the usefulness of the proposed estimator.

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