Weighted Nadaraya--Watson Estimation of Conditional Expected Shortfall

Kengo Kato

Journal of Financial Econometrics, 2012, vol. 10, issue 2, 265-291

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. Copyright The Author 2012. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com., Oxford University Press.

Date: 2012
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