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Systemic Risk: Conditional Distortion Risk Measures

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  • Jan Dhaene
  • Roger J. A. Laeven
  • Yiying Zhang

Abstract

In this paper, we introduce the rich classes of conditional distortion (CoD) risk measures and distortion risk contribution ($\Delta$CoD) measures as measures of systemic risk and analyze their properties and representations. The classes include the well-known conditional Value-at-Risk, conditional Expected Shortfall, and risk contribution measures in terms of the VaR and ES as special cases. Sufficient conditions are presented for two random vectors to be ordered by the proposed CoD-risk measures and distortion risk contribution measures. These conditions are expressed using the conventional stochastic dominance, increasing convex/concave, dispersive, and excess wealth orders of the marginals and canonical positive/negative stochastic dependence notions. Numerical examples are provided to illustrate our theoretical findings. This paper is the second in a triplet of papers on systemic risk by the same authors. In \cite{DLZorder2018a}, we introduce and analyze some new stochastic orders related to systemic risk. In a third (forthcoming) paper, we attribute systemic risk to the different participants in a given risky environment.

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  • Jan Dhaene & Roger J. A. Laeven & Yiying Zhang, 2019. "Systemic Risk: Conditional Distortion Risk Measures," Papers 1901.04689, arXiv.org, revised Jan 2019.
    • Handle: RePEc:arx:papers:1901.04689
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    3. Bingzhen Geng & Yang Liu & Yimiao Zhao, 2024. "Value-at-Risk- and Expectile-based Systemic Risk Measures and Second-order Asymptotics: With Applications to Diversification," Papers 2404.18029, arXiv.org.
    4. Ye, Wuyi & Zhou, Yi & Chen, Pengzhan & Wu, Bin, 2024. "A simulation-based method for estimating systemic risk measures," European Journal of Operational Research, Elsevier, vol. 313(1), pages 312-324.
    5. Zang, Xin & Jiang, Fan & Xia, Chenxi & Yang, Jingping, 2024. "Random distortion risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 116(C), pages 51-73.
    6. Zhang, Yiying, 2024. "Stochastic orders and distortion risk contribution ratio measures," Insurance: Mathematics and Economics, Elsevier, vol. 118(C), pages 104-122.
    7. Hirbod Assa & Peng Liu, 2024. "Factor risk measures," Papers 2404.08475, arXiv.org.
    8. Aleksy Leeuwenkamp & Wentao Hu, 2023. "New general dependence measures: construction, estimation and application to high-frequency stock returns," Papers 2309.00025, arXiv.org.
    9. Tong Pu & Yifei Zhang & Yiying Zhang, 2024. "On Joint Marginal Expected Shortfall and Associated Contribution Risk Measures," Papers 2405.07549, arXiv.org.
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