Nonparametric kernel estimation of CVaR under $$\alpha $$α-mixing sequences

Zhongde Luo ()
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Zhongde Luo: Baise University

Statistical Papers, 2020, vol. 61, issue 2, No 5, 615-643

Abstract: Abstract Conditional Value-at-Risk (CVaR) is an increasingly popular coherent risk measure in financial risk management. In this paper, a new nonparametric kernel estimator of CVaR is established, and a Bahadur type expansion of the estimator is also given under $$\alpha $$α-mixing sequences. Furthermore, the mean, variance, mean square error (MSE) and uniformly asymptotic normality of the new estimator are discussed, optimal bandwidths are obtained as well. In order to better illustrate performances of the new CVaR estimator, we conduct numerical simulations under some $$\alpha $$α-mixing sequences and a GARCH model, and discover that the new CVaR estimator is smoother and more accurate than estimators proposed by other scholars because of the bias and MSE of the new estimator are smaller. Finally, we use the new estimator to analyze the daily log-loss of real financial series.

Keywords: Nonparametric kernel estimator; CVaR; $$\alpha $$ α -Mixing sequence; Bahadur type expansion; Uniformly asymptotic normality; MSE; Optimal bandwidth; 62G05; 62G20; 62E20 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s00362-017-0952-2

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