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<p>The expectile-based value-at-risk (EVaR) has been attracted attention recently in financial risk management, because it is the only coherent and elicitable risk measure. However, since there is no closed-form solution for minimizing the expectile-loss function, the existing nonparametric estimator for EVaR usually requires an additional iterative algorithm. This paper presents a new alternative nonparametric estimator for EVaR for dependent financial returns. The proposed estimator is computationally easy to implement by existing software, without any extra iterative computation burdens. We also establish its asymptotic properties for statistical inference, including the strong consistency and asymptotic normality. Monte Carlo simulations demonstrate its good performance being comparable to the existing estimator in terms of bias and mean squared error, but outperforming the existing estimator in terms of computational efficiency. Two empirical applications of the US dollar index data and S&amp;P500 index data are conducted to illustrate the method. The results show that our proposed estimator is better than compared estimator in EVaRs forecasting with smaller associated realized losses and less computation time.</p>

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A Direct Nonparametric Estimator for EVaR of Dependent Financial Returns

  • 期刊论文

  • 发表日期：

    2025年3月5日

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  • Feipeng Zhang,
  • Yuhan Ma,
  • Yongchang Hui

摘要

The expectile-based value-at-risk (EVaR) has been attracted attention recently in financial risk management, because it is the only coherent and elicitable risk measure. However, since there is no closed-form solution for minimizing the expectile-loss function, the existing nonparametric estimator for EVaR usually requires an additional iterative algorithm. This paper presents a new alternative nonparametric estimator for EVaR for dependent financial returns. The proposed estimator is computationally easy to implement by existing software, without any extra iterative computation burdens. We also establish its asymptotic properties for statistical inference, including the strong consistency and asymptotic normality. Monte Carlo simulations demonstrate its good performance being comparable to the existing estimator in terms of bias and mean squared error, but outperforming the existing estimator in terms of computational efficiency. Two empirical applications of the US dollar index data and S&P500 index data are conducted to illustrate the method. The results show that our proposed estimator is better than compared estimator in EVaRs forecasting with smaller associated realized losses and less computation time.