杨梦兰, 杨淑振. 次线性期望下ES的计算和实证分析[J]. 应用概率统计, 2023, 39(4): 623-632. DOI: 10.3969/j.issn.1001-4268.2023.04.011
引用本文: 杨梦兰, 杨淑振. 次线性期望下ES的计算和实证分析[J]. 应用概率统计, 2023, 39(4): 623-632. DOI: 10.3969/j.issn.1001-4268.2023.04.011
YANG Menglan, YANG Shuzhen. ES under Sublinear Expectation and Related Experiment[J]. Chinese Journal of Applied Probability and Statistics, 2023, 39(4): 623-632. DOI: 10.3969/j.issn.1001-4268.2023.04.011
Citation: YANG Menglan, YANG Shuzhen. ES under Sublinear Expectation and Related Experiment[J]. Chinese Journal of Applied Probability and Statistics, 2023, 39(4): 623-632. DOI: 10.3969/j.issn.1001-4268.2023.04.011

次线性期望下ES的计算和实证分析

ES under Sublinear Expectation and Related Experiment

  • 摘要: 在金融市场中, VaR和ES被广泛应用于资产风险度量、投资组合管理和保证金计算等方面, 是银行资本和风险监管的国际统一标准.由于VaR具有一定的局限性, 近年来,ES作为一种重要的风险度量方法深受金融机构关注. 本文基于次线性期望理论,在G-VaR的基础上, 提出了一种新的G-ES的计算方法,这种计算方法可以很自然地结合G-VaR进行回测.对于标普500指数以及沪深~300~指数数据, 与其他常用的模型, 如历史模拟,AR-GARCH模型, 基于极值理论的POT模型等进行比较,实证分析的结果表明这一新型的G-ES在不同历史数据窗口下都有着很好的表现.

     

    Abstract: In financial market, VaR and ES are applied to measure the risk of asset, portfolio management and margin calculation, which are the international unified standards for bank capital and risk supervision. However, VaR has some certain limitations, ES, as an important risk measurement method, has attracted the attention of financial institutions in recent years. Based on the sublinear expectation theory and G-VaR, this study proposes a new calculation method for ES, and denoted as G-ES. This calculation method can be naturally combined with the back testing of G-VaR. Based on the data of S\&P 500 index and CSI300 index, comparing with other commonly used models, such as historical simulation, AR-GARCH model and POT model based on extreme value theory, it is found that this G-ES method has a good performance within different historical data windows.

     

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