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Econometric modeling of risk measures: A selective review of the recent literature

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Applied Mathematics(A Journal of Chinese Universities) 2019年第2期34卷 205-228页

作者： TIAN Ding-shi CAI Zong-wu FANG Ying Wang Yanan Institute for Studies in Economics Department of StatisticsSchool of EconomicsMinistry of Education Key Laboratory of Econometrics and Fujian Key Laboratory of Statistical ScienceXiamen UniversityXiamenFujian 361005China Department of Economics University of KansasLawrenceKS 66045USA

Since the financial crisis in 2008, the risk measures which are the core of risk management, have received increasing attention among economists and practitioners. In this review, the concentration is on recent developments in the estimation of the most popular risk measures, namely, value at risk (VaR), expected shortfall (ES), and expectile. After introducing the concept of risk measures, the focus is on discussion and comparison of their econometric modeling. Then, parametric and nonparametric estimations of tail dependence are investigated. Finally, we conclude with insights into future research directions.

关键词： Expectile Expected shortfall Network Risk Nonparametric Estimation Tail Dependence Value at Risk

Adjexpectile风险测度的性质、优化及资产配置的应用

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中国管理科学 2018年第5期26卷 51-61页

作者：周静罗乐华中科技大学管理学院

金融风险的度量和识别是风险管理的重要内容,常用的风险度量工具是标准差、VaR、ES,但存在很多缺陷,expectile的提出弥补了这些不足,在理论界得到广泛的讨论和应用。本文扩展了expectile进行资产配置,提出Adjexpectile的概念,并讨论和... 详细信息

金融风险的度量和识别是风险管理的重要内容,常用的风险度量工具是标准差、VaR、ES,但存在很多缺陷,expectile的提出弥补了这些不足,在理论界得到广泛的讨论和应用。本文扩展了expectile进行资产配置,提出Adjexpectile的概念,并讨论和分析了Adjexpectile的一致性风险度量、随机占优性、凸性,与标准差、VaR、shortfall的关系,风险贡献及风险分解的性质。通过对六个资产指数：上证国债指数、上证企业债指数、上证180指数、深圳100指数、深成长40p指数和黄金现货指数的复合周收益率数据进行组合优化配置,发现Adjexpectile在非对称性收益数据、组合前沿、风险分散方面具有一定的优越性。

关键词： Adjexpectile Expectile shortfall VaR 资产配置非对称最小二乘

Stress Testing of Liquidity Maturity Transformation Risk in Banks

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Management Studies 2018年第4期6卷 235-251页

作者： Eugenia Schmitt FinRiskConsult MunichGermany

One of the main causes of the past crisis was the inability of financial institutions to acquire funding at appropriate *** importance of applying a good liquidity risk measurement system becomes *** present paper provides an approach to the measurement of liquidity maturity transformation risk within a stress testing framework,for middle-sized *** costs of liquidity arising due to a downturn in refinancing conditions are calculated by using modern risk *** forward-looking way is based on a liquidity gap report,where the consideration of the counterbalancing capacity enables to gain an insight into the real liquidity *** measurement of both,the portfolio-value in the respective time bucket and liquidity costs,is *** the expected shortfall can easily be included into the *** results show that by using historical simulation,if no sufficient data are available,expected shortfall delivers an approximate ***,it can serve as an indicator of insurance against extreme *** present approach combines a scenario-based view to a possible distress with a quantitative risk ***,it contributes to the bank’s wide stress testing as required by the regulatory authorities.

关键词： liquidity risk stress testing value at risk expected shortfall funding risk banking historical simulation,spread risk regulatory requirements

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资产相关结构对投资组合风险测度的影响分析

统计与决策 2008年第19期24卷 38-40页

作者：任仙玲叶明确张世英天津大学管理学院天津300072 上海大学国际工商与管理学院上海200444

文章从分析金融资产收益率的统计特征入手,以GARCH模型为基础,用非对称幂分布描述组合资产中各金融资产收益率的边缘分布函数,在多种Copula函数情形下计算组合资产的风险值VaR及ES。结果表明:基于由多元Clayton Copula和多元Gumbel Cop... 详细信息

文章从分析金融资产收益率的统计特征入手,以GARCH模型为基础,用非对称幂分布描述组合资产中各金融资产收益率的边缘分布函数,在多种Copula函数情形下计算组合资产的风险值VaR及ES。结果表明:基于由多元Clayton Copula和多元Gumbel Copula组成的混合Copula函数较好地刻画了多只股票的相关结构,而且ES比VaR能够较准确地估计组合资产的尾部风险。

关键词： GAKCH模型 Value-at-risk 非对称幂分布:多元Copula函数 Expected shortfall

Further Results about Calibration of Longevity Risk for the Insurance Business

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Applied Mathematics 2014年第4期5卷 653-657页

作者： Mariarosaria Coppola Valeria D’Amato Department of Political Sciences Federico II University Naples Italy Department of Statistics and Economics Campus di Fisciano University of Salerno Salerno Italy

In life insurance business, longevity risk, i.e. the risk that the insured population lives longer than the expected, represents the heart of the risk assessment, having significant impact in terms of solvency capital requirements (SCRs) needed to front the firm obligations. The credit crisis has shown that systemic risk as longevity risk is relevant and that for many insurers it is actually the dominant risk. With the adoption of the Solvency II directive, a new area for insurance in terms of solvency regulation has been opened up. The international guidelines prescribe a market consistent valuation of balance sheets, where the solvency capital requirements to be set aside are calculated according to a modular structure. By mapping the main risk affecting the insurance portfolio, the capital amount able to cover the liabilities corresponds to each measured risk. In Solvency II, the longevity risk is included into underwriting risk module. In particular, the rules propose that companies use a standard model for measuring the SCRs. Nevertheless, the legislation under consideration allows designing tailor-made internal models. As regards the longevity risk assessment, the regulatory standard model leads to noteworthy inconsistencies. In this paper, we propose a stochastic volatility model combined with a so-called coherent risk measure as the expected shortfall for measuring the SCRs according to more realistic assumptions on future evolution of longevity trend. Finally empirical evidence is provided.

关键词： Solvency II Solvency Capital Requirement Longevity Risk Longevity Shocks Expected shortfall

SV-t模型下人民币汇率VaR和ES的动态度量与分析

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商业时代 2013年第12期 65-67页

作者：陈丽娟上海商学院财经学院金融系

人民币汇率的风险度量是汇率风险管理的关键环节。本文首先用SV-t模型对人民币对美元、日元及欧元汇率收益的波动率进行分析,在此基础上分别运用VaR和ES方法对其风险进行动态的度量与分析比较。结果表明:SV-t模型能够刻画出人民币汇率... 详细信息

人民币汇率的风险度量是汇率风险管理的关键环节。本文首先用SV-t模型对人民币对美元、日元及欧元汇率收益的波动率进行分析,在此基础上分别运用VaR和ES方法对其风险进行动态的度量与分析比较。结果表明:SV-t模型能够刻画出人民币汇率收益率序列的波动特征;人民币对美元的VaR基本反映出其最大可能的损失;人民币对日元及欧元的Va R则低估了实际的风险水平,相应的ES虽保守却比较准确地估计出尾部风险。文章最后也对中国汇率市场的风险管理及风险监管提出了一些政策建议。

关键词：人民币汇率 SV—t模型学生t分布 Value—at—Risk Expected shortfall

SV-GED模型在中国股市的VaR与ES度量及分析

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系统工程理论方法应用 2006年第1期15卷 44-48页

作者：李付军东南大学经济管理学院南京210096

从分析中国股市指数收益率的统计特征入手,以SV模型为基础,在多种分布情形下测算了沪深两市时变风险值V aR及ES。结果表明:基于GED分布的SV模型(SV-GED模型)较好地刻画了高频时间序列的尖峰肥尾性及波动集聚性与持续性等特性,并对两市... 详细信息

从分析中国股市指数收益率的统计特征入手,以SV模型为基础,在多种分布情形下测算了沪深两市时变风险值V aR及ES。结果表明:基于GED分布的SV模型(SV-GED模型)较好地刻画了高频时间序列的尖峰肥尾性及波动集聚性与持续性等特性,并对两市指数进行较准确的预测,ES相比V aR能够较准确地估计尾部风险。

关键词：随机波动模型 Value-at-Risk 广义误差分布 Expected shortfall

基于ARMA-GARCH模型创业板市场风险VaR和ES实证研究

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基于ARMA-GARCH模型创业板市场风险VaR和ES实证研究

作者：齐肖阳南昌大学

学位级别：硕士

本文主要是讨论风险度量新方法ES的基本原理;基于ARMA-GARCH模型展开对我国创业板市场日收盘价对数收益率的市场风险实证分析，计算其VaR值和ES值来度量创业板指数的市场风险;此外，也运用向量自回归模型探讨创业板和中小板的相互影响... 详细信息

本文主要是讨论风险度量新方法ES的基本原理;基于ARMA-GARCH模型展开对我国创业板市场日收盘价对数收益率的市场风险实证分析，计算其VaR值和ES值来度量创业板指数的市场风险;此外，也运用向量自回归模型探讨创业板和中小板的相互影响，深度分析创业板的风险因素。全文共分5章。第一章介绍本文研究主要内容的背景、意义和方法，简要叙述VaR和ES相关历史文献。第二章主要介绍ES基本原理。采用资产组合损失变量描述风险，并基于损失分布的-（上）分位数给出“期望巨额损失值”ES（Expected shortfall）和“条件风险价值”CVaR（Conditional Value at Risk）的定义。在一般损失分布下，通过直接计算说明了任一资产组合损失变量的“期望巨额损失值”ES的定义与-（上）分位数的选取无关;而且也通过直接计算证明了ES与CVaR两者的等价关系;进而通过构造出ES的概率测度族表示证明了ES是一致性风险度量方法。第三章基于ARMA-GARCH模型，运用风险度量的VaR和ES方法对创业板指数（样本：2010.6.1-2014.2.1）的市场风险进行实证分析，包括VaR、ES的计算问题、比较分析等。首先对创业板块日收盘指数之间的自然对数收益率进行基本统计分析，发现序列的分布存在厚尾的特征;运用AIC+SC准则确定各模型的滞后阶数。对各模型的参数进行估计，得到残差序列，进一步得到残差序列的VaR值，并根据模型的数学表达式得到最终的VaR值和ES值。最后利用失败率检验法，对模型进行检验。实证的结果表明，ES在VaR估计失败时，能比较准确地估计例外情形的实际损失，即ES可以用来弥补VaR模型的缺点，ES是比VaR更加稳健和保守的风险度量方法。第四章运用VAR（向量自回归）模型，研究创业板收盘指数和中小板收盘指数的相互影响。通过协整以及格兰杰因果检验，分析创业板和中小板之间的内在关系，寻找影响创业板风险的外部因素。结果表明，它们的波动性是比较一致的;中小板和创业板之间不存在长期均衡关系。研究结果进一步表明，创业板对中小板的影响要大一些。第五章是对全文进行的总结并指出了文中的不足以及对今后研究方向的展望。

关键词： VaR Expected shortfall ARMA模型 GARCH族模型向量自回归模型 LR检验协整检验

On Bounds of Value-at-Risk and Convex Risk Measure of Portfolio of Weighted Dependent Risks

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Chinese Quarterly Journal of Mathematics 2018年第4期33卷 421-433页

作者： XING Guo-dong LI Xiao-hu School of Mathematics & Computer Science Shangrao Normal University Shangrao 334001China School of Mathematical Sciences Xiamen University Xiamen 361005China Department of Mathematical Sciences Stevens Institute of Technology HobokenNJ 07030USA

This note analytically derives lower and upper bounds for Value-at-Risk and convex risk measures of a portfolio of weighted risks in the context of positive *** bounds serve as extensions of the corresponding ones due to Bignozzi et al.(2015).Also, DU-spread of value-at-risk and expected shortfall of Bignozzi et al.(2015) are also improved in some particular cases.

关键词： DU-spread Expected shortfall Lower orthant order Upper orthant order Weakly conditional increasing in sequence order