The Conditional Value-at-Risk (CVaR) is a coherent measure that evaluates the risk for different investing scenarios. On the other hand, since the extreme value distribution has been revealed to furnish better financial and economical data adjustment in contrast to the well-known normal distribution, we here employ this distribution in investigating explicit formulas for the two common risk measures, i.e., VaR and CVaR, to have better tools in risk management. The formulas are then employed under the generalized autoregressive conditional heteroskedasticity (GARCH) model for risk management as our main contribution. To confirm the theoretical discussions of this work, the daily returns of several stocks are considered and worked out. The simulation results uphold the superiority of our findings.

中文翻译：

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金融中采用肥尾分布管理风险的统计GARCH模型

条件风险价值 (CVaR) 是一种连贯的衡量标准，用于评估不同投资场景的风险。另一方面，由于与众所周知的正态分布相比，极值分布已被揭示可以提供更好的金融和经济数据调整，因此我们在这里采用这种分布来研究两种常见风险度量的显式公式，即 VaR和 CVaR，以获得更好的风险管理工具。然后在广义自回归条件异方差（GARCH）模型下使用这些公式进行风险管理，作为我们的主要贡献。为了证实这项工作的理论讨论，考虑并计算了几只股票的每日收益。模拟结果证明了我们发现的优越性。