POT-SGEL模型在金融极端尾部风险中的应用

Application of the POT-SGEL Model to Financial Extreme Tail Risk

在金融市场中,极端事件往往会对投资者造成较大的损失,建立有效的极端值模型可以降低极端风险对投资者产生的影响。本文考虑了极端尾部风险的情况,基于极值理论和SGEL分布,将POT模型中的超额分布用SGEL分布近似,提出了POT-SGEL模型;应用POT-SGEL模型来估计标普100指数日对数收益率的极端VaR值;通过与POT模型进行对比发现,POT-SGEL模型能够对极端VaR值进行估计,且在一定程度上比POT模型更优。In financial markets, extreme events tend to cause large losses to investors, and modelling effective extremes can reduce the impact of extreme risks on investors. This article considers the case of extreme tail risk, and based on the extreme value theory and SGEL distribution, the excess distribution in the POT model is approximated by the SGEL distribution, and the POT-SGEL model is proposed;the POT-SGEL model is applied to estimate the extreme VaR values of the daily log returns of the S&P 100 index;through comparison with the POT model, it is found that the POT-SGEL model is able to estimate the extreme VaR values and is to some extent better than the POT model.