Nonparametric Estimation of Conditional VaR and Expected Shortfall
Zongwu Cai, Xian Wang
#002095 20131014 (published)
This paper considers a new nonparametric estimation of conditional value-at-risk and expected shortfall functions. Conditional value-at-risk is estimated by inverting the weighted double kernel local linear estimate of the conditional distribution function. The nonparametric estimator of conditional expected shortfall is constructed by a plugging-in method. Both the asymptotic normality and consistency of the proposed nonparametric estimators are established at both boundary and interior points for time series data. We show that the weighted double kernel local linear conditional distribution estimator has the advantages of always being a distribution, continuous, and differentiable, besides the good properties from both the double kernel local linear and weighted Nadaraya-Watson estimators. Moreover, an adhoc data-driven fashion bandwidth selection method is proposed, based on the nonparametric version of the Akaike information criterion. Finally, an empirical study is carried out to illustrate the finite sample performance of the proposed estimators. Published by Elsevier B.V.
JEL-Codes: C14 D81 G10 G22 G31
Keywords: Boundary effects, Empirical likelihood, Expected shortfall, Local linear estimation,Nonparametric smoothing, Value-at-risk, Weighted double kernel

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