ISSN 0253-2778

CN 34-1054/N

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Open AccessOpen Access JUSTC Original Paper

Dynamic systematic tail risk measurement based on tail index regression

  • 1.

    Department of Statistics and Finance, School of Management, University of Science and Technology of China, Hefei 230026, China

  • 2.

    International Institute of Finance, University of Science and Technology of China, Hefei 230601, China

Cite this:
https://doi.org/10.3969/j.issn.0253-2778.2020.02.013
  • Received Date: 07 March 2019
  • Accepted Date: 09 April 2019
  • Rev Recd Date: 09 April 2019
  • Publish Date: 28 February 2020
    Abstract

  • Abstract

    The impact of the （volatility index,VIX) on the tail index was considered based on the regression model. The relationship between the tail index and the systematic tail risk coefficient was studied and a time-varying dynamic systematic tail risk coefficient model was established. Based on the model, the CVaR and the time-varying tail systematic tail risk coefficient of typical stock indices of eight countries were studied. The results show that during the financial crisis, the tail risk of the global market had increased significantly. The systematic tail risks of typical stock indices of China, Japan, Russia, India, France, and England were less than those of the global market, while those of the United States and Germany were higher.

    Abstract

    The impact of the （volatility index,VIX) on the tail index was considered based on the regression model. The relationship between the tail index and the systematic tail risk coefficient was studied and a time-varying dynamic systematic tail risk coefficient model was established. Based on the model, the CVaR and the time-varying tail systematic tail risk coefficient of typical stock indices of eight countries were studied. The results show that during the financial crisis, the tail risk of the global market had increased significantly. The systematic tail risks of typical stock indices of China, Japan, Russia, India, France, and England were less than those of the global market, while those of the United States and Germany were higher.
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    • References(16)
  • [1]
    HILL B M. A simple general approach to inference about the tail of a distribution[J]. The Annals of Statistics, 1975:1163-1174.
    [2]
    BEIRLANT J, GOEGEBEUR Y. Regression with response distributions of Pareto-type[J]. Computational Statistics & Data Analysis, 2003, 42(4): 595-619.
    [3]
    WANG H, TSAI C L. Tail index regression[J]. Journal of the American Statistical Association, 2009, 104(487):1233-1240.
    [4]
    陈向红. 重尾分布尾部指数的 Crovella 估计性质研究[J]. 南京工程学院学报 (自然科学版), 2008, 6(3):7-11.
    CHEN Xianghong.Study on property of Crovella estimation of heavy tailed distribution index[J]. Journal of Nanjing Institute of Technology (Natural Science Edition), 2008, 6(3):7-11.
    [5]
    孙美美. 具有 GARCH 误差项的单位根模型尾部指数的区间估计[D]. 杭州: 浙江大学, 2014.
    [6]
    庞素琳, 吴曼琪. 股指期货保证金水平设置比较研究——基于Hill及VaR-x估计法[J]. 管理科学学报, 2014, 17(6):84-96.
    PANG Sulin, WU Manqi. Margin level setting of stock index futures based on Hill estimation and VaR-x estimation[J]. Journal of Management Sciences in China, 2014, 17(6):84-96.
    [7]
    HALL P. Using the bootstrap to estimate mean squared error and select smoothing parameter in nonparametric problems[J]. Journal of Multivariate Analysis, 1990, 32(2):177-203.
    [8]
    刘维奇, 赫英迪, 邢红卫. 选择重尾阈值k的Bootstrap方法[J].山西大学学报(自然科学版), 2010, 33(4): 508-512.
    LIU Weiqi, HE Yingdi, XING Hongwei. Bootstrap method in selecting heavy-tailed threshold k[J]. Journal of Shanxi University (Natural Science Edition), 2010, 33(4): 508-512.
    [9]
    ACHARYA V V, PEDERSEN L H, PHILIPPON T, et al. Measuring systemic risk[J]. The Review of Financial Studies, 2017, 30(1): 2-47.
    [10]
    ADRIAN T,BRUNNERMEIER M. Risk spillovers of financial institutions[R/OL]. [2019-01-01]. https://conference.nber.org/conferences/2008/si2008/Risk/adrian.pdf.
    [11]
    ADRIAN T, BRUNNERMEIER M K. CoVAR[R]. Cambridge， MA: National Bureau of Economic Research, 2011: No. 17454.
    [12]
    高国华, 潘英丽. 银行系统性风险度量——基于动态 CoVaR方法的分析[J]. 上海交通大学学报, 2011, 45(12): 1753-1759.
    GAO Guohua, PAN Yingli.Banking systemic risk based on dynamic CoVaR estimation[J]. Journal of Shanghai Jiaotong University, 2011, 45(12): 1753-1759.
    [13]
    陈国进, 钟灵, 张宇. 我国银行体系的系统性关联度分析: 基于不对称 CoVaR[J]. 系统工程理论与实践, 2017, 37(1):61-79.
    CHEN Guojin, ZHONG Ling, ZHANG Yu. Systemic linkages in the Chinese banking system: The asymmetric CoVaR approach[J]. Systems Engineering:Theory & Practice, 2017, 37(1):61-79.
    [14]
    HARLOW W V, RAO R K S. Asset pricing in a generalized mean-lower partial moment framework: Theory and evidence[J]. Journal of Financial and Quantitative Analysis, 1989, 24(3): 285-311.
    [15]
    VAN OORDT M R, ZHOU C. Systematic tail risk[J]. Journal of Financial and Quantitative Analysis, 2016, 51(2):685-705.
    [16]
    叶五一, 张明, 缪柏其. 基于尾部指数回归方法的 CVaR 估计以及实证研究[J]. 统计研究, 2012, 29(11):79-83.
    YE Wuyi, ZHANG Ming, MIAO Baiqi. Estimation of CVaR and empirical analysis based on tail index regression model[J]. Statistical Research, 2012, 29(11):79-83.)
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    [1]
    HILL B M. A simple general approach to inference about the tail of a distribution[J]. The Annals of Statistics, 1975:1163-1174.
    [2]
    BEIRLANT J, GOEGEBEUR Y. Regression with response distributions of Pareto-type[J]. Computational Statistics & Data Analysis, 2003, 42(4): 595-619.
    [3]
    WANG H, TSAI C L. Tail index regression[J]. Journal of the American Statistical Association, 2009, 104(487):1233-1240.
    [4]
    陈向红. 重尾分布尾部指数的 Crovella 估计性质研究[J]. 南京工程学院学报 (自然科学版), 2008, 6(3):7-11.
    CHEN Xianghong.Study on property of Crovella estimation of heavy tailed distribution index[J]. Journal of Nanjing Institute of Technology (Natural Science Edition), 2008, 6(3):7-11.
    [5]
    孙美美. 具有 GARCH 误差项的单位根模型尾部指数的区间估计[D]. 杭州: 浙江大学, 2014.
    [6]
    庞素琳, 吴曼琪. 股指期货保证金水平设置比较研究——基于Hill及VaR-x估计法[J]. 管理科学学报, 2014, 17(6):84-96.
    PANG Sulin, WU Manqi. Margin level setting of stock index futures based on Hill estimation and VaR-x estimation[J]. Journal of Management Sciences in China, 2014, 17(6):84-96.
    [7]
    HALL P. Using the bootstrap to estimate mean squared error and select smoothing parameter in nonparametric problems[J]. Journal of Multivariate Analysis, 1990, 32(2):177-203.
    [8]
    刘维奇, 赫英迪, 邢红卫. 选择重尾阈值k的Bootstrap方法[J].山西大学学报(自然科学版), 2010, 33(4): 508-512.
    LIU Weiqi, HE Yingdi, XING Hongwei. Bootstrap method in selecting heavy-tailed threshold k[J]. Journal of Shanxi University (Natural Science Edition), 2010, 33(4): 508-512.
    [9]
    ACHARYA V V, PEDERSEN L H, PHILIPPON T, et al. Measuring systemic risk[J]. The Review of Financial Studies, 2017, 30(1): 2-47.
    [10]
    ADRIAN T,BRUNNERMEIER M. Risk spillovers of financial institutions[R/OL]. [2019-01-01]. https://conference.nber.org/conferences/2008/si2008/Risk/adrian.pdf.
    [11]
    ADRIAN T, BRUNNERMEIER M K. CoVAR[R]. Cambridge， MA: National Bureau of Economic Research, 2011: No. 17454.
    [12]
    高国华, 潘英丽. 银行系统性风险度量——基于动态 CoVaR方法的分析[J]. 上海交通大学学报, 2011, 45(12): 1753-1759.
    GAO Guohua, PAN Yingli.Banking systemic risk based on dynamic CoVaR estimation[J]. Journal of Shanghai Jiaotong University, 2011, 45(12): 1753-1759.
    [13]
    陈国进, 钟灵, 张宇. 我国银行体系的系统性关联度分析: 基于不对称 CoVaR[J]. 系统工程理论与实践, 2017, 37(1):61-79.
    CHEN Guojin, ZHONG Ling, ZHANG Yu. Systemic linkages in the Chinese banking system: The asymmetric CoVaR approach[J]. Systems Engineering:Theory & Practice, 2017, 37(1):61-79.
    [14]
    HARLOW W V, RAO R K S. Asset pricing in a generalized mean-lower partial moment framework: Theory and evidence[J]. Journal of Financial and Quantitative Analysis, 1989, 24(3): 285-311.
    [15]
    VAN OORDT M R, ZHOU C. Systematic tail risk[J]. Journal of Financial and Quantitative Analysis, 2016, 51(2):685-705.
    [16]
    叶五一, 张明, 缪柏其. 基于尾部指数回归方法的 CVaR 估计以及实证研究[J]. 统计研究, 2012, 29(11):79-83.
    YE Wuyi, ZHANG Ming, MIAO Baiqi. Estimation of CVaR and empirical analysis based on tail index regression model[J]. Statistical Research, 2012, 29(11):79-83.)
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