Returns in financial assets display consistent excess kurtosis and skewness, implying the presence of large fluctuations not forecasted by Gaussian models. This paper applies a resampling method based on the bootstrap and a bias-correction step to improve Value-at-Risk (VaR) forecasting ability of the n-EGARCH (normal EGARCH) model and correct the VaR for both long and short positions. Our aim is to utilize the advantages of this model, but still use the bootstrap resampling method to accurate for the tendency of the model tomiscalculate the VaR. Empirical results indicate that the bias-correction method can improve the n-GARCH and n-EGARCH VaR forecasts so much that the acquired VaR predictions are different from the proposed probability. Additionally, allowing asymmetry in the conditional variance using the EGARCH model with normal distribution instead of GARCH improves the performance of the bias-correction method in forecasting the VaR for almost all considered indices. Moreover, the bias-corrected n-EGARCH model performs better than the simple t-EGARCH model. Thus, it seems that this model can take account of both the asymmetry in the conditional variance and leptokurtosis in returns distribution. However, we find that the superiority of the bias-corrected n-EGARCH model over the t-EGARCH model is not completely confirmed for short positions based on the censored likelihood scoring rule.

中文翻译：

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从正常的 EGARCH 模型改进风险价值估计

金融资产的回报显示出一致的超峰度和偏度，这意味着存在高斯模型无法预测的大波动。本文应用基于引导程序和偏差校正步骤的重采样方法来提高 n-EGARCH（正常 EGARCH）模型的风险价值 (VaR) 预测能力，并校正多头和空头头寸的 VaR。我们的目标是利用该模型的优点，但仍然使用bootstrap重采样方法来准确预测模型错误计算VaR的趋势。实证结果表明，偏差校正方法可以大大改善 n-GARCH 和 n-EGARCH VaR 预测，以至于获得的 VaR 预测与建议的概率不同。此外，使用具有正态分布的 EGARCH 模型而不是 GARCH 允许条件方差的不对称性提高了偏差校正方法在预测几乎所有考虑指标的 VaR 时的性能。此外，偏差校正的 n-EGARCH 模型比简单的 t-EGARCH 模型表现更好。因此，该模型似乎可以同时考虑条件方差的不对称性和收益分布的峰态。然而，我们发现基于删失似然评分规则的空头头寸并没有完全证实偏差校正的 n-EGARCH 模型优于 t-EGARCH 模型。偏差校正的 n-EGARCH 模型比简单的 t-EGARCH 模型表现更好。因此，该模型似乎可以同时考虑条件方差的不对称性和收益分布的峰态。然而，我们发现基于删失似然评分规则的空头头寸并没有完全证实偏差校正的 n-EGARCH 模型优于 t-EGARCH 模型。偏差校正的 n-EGARCH 模型比简单的 t-EGARCH 模型表现更好。因此，该模型似乎可以同时考虑条件方差的不对称性和收益分布的峰态。然而，我们发现基于删失似然评分规则的空头头寸并没有完全证实偏差校正的 n-EGARCH 模型优于 t-EGARCH 模型。