Value-at-risk (VaR) is a crucial subject that researchers and practitioners extensively use to measure and manage uncertainty in financial markets. Although VaR is a standard risk control instrument, there are criticisms about its performance. One of these cases, which has been studied in this research, is the VaR underestimation during times of crisis. In these periods, the non-Gaussian behavior of markets intensifies, and the estimated VaRs by typical models are lower than the real values. A potential approach that can be used to describe the non-Gaussian behavior of return series is the Tsallis entropy framework and nonextensive statistical methods. This paper has used the nonextensive models for analyzing financial markets’ behavior during crisis times. By applying the q-Gaussian probability density function for emerging and mature markets over 20 years, we can see a better VaR estimation than the regular models, especially during crisis times. We have shown that the q-Gaussian models composed of VaR and Expected Shortfall (ES) estimate risk better than the standard models. By comparing the ES, VaR, q-VaR and q-ES for emerging and mature markets, we see in confidence levels more than 0.98, the outputs of q models are more real, and the q-ES model has lower errors than the other ones. Also, it is evident that in the mature markets, the difference of VaR between normal condition and nonextensive approach increases more than one standard deviation during times of crisis. Still, in the emerging markets, we cannot see a specific pattern. The findings of this paper are useful for analyzing the risk of financial crises in different markets.

中文翻译：

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危机时期的非广泛风险价值估计

风险价值 (VaR) 是研究人员和从业人员广泛用于衡量和管理金融市场不确定性的关键主题。尽管 VaR 是一种标准的风险控制工具，但对其表现也存在批评。本研究中研究的其中一个案例是危机时期的风险价值低估。在这些时期，市场的非高斯行为加剧，典型模型估计的 VaR 低于实际值。可用于描述回报序列的非高斯行为的一种潜在方法是 Tsallis 熵框架和非扩展统计方法。本文使用非扩展模型来分析金融市场在危机时期的行为。通过应用q- 20 多年来新兴市场和成熟市场的高斯概率密度函数，我们可以看到比常规模型更好的 VaR 估计，尤其是在危机时期。我们已经证明了q- 由 VaR 和预期短缺 (ES) 组成的高斯模型比标准模型更好地估计风险。通过比较 ES、VaR、q-VaR 和q-ES 对于新兴市场和成熟市场，我们看到置信水平超过 0.98，产出q模型更真实，并且q-ES 模型的误差低于其他模型。此外，很明显，在成熟市场中，正常情况下的 VaR 与非扩展方法之间的差异在危机时期会增加一个以上的标准差。不过，在新兴市场，我们看不到具体的模式。本文的研究结果有助于分析不同市场的金融危机风险。