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Three regime bivariate normal distribution: a new estimation method for co-value-at-risk, CoVaR

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  • Ji-Eun Choi
  • Dong Wan Shin

Abstract

We propose a new distribution for estimation of co-value-at-risk, CoVaR, a financial system risk measure conditional on an institution in a financial distress: a three regime bivariate normal (3RN) distribution which is composed of three bivariate normal distributions with asymmetric variance matrices for the right-tail, left-tail and mid-part corresponding to the return of an institution. The distribution captures explicitly the asymmetric correlation of system return and institution return: usually stronger for bad times than for good times. The 3RN distribution allows simple evaluations of the CoVaR taking full advantage of asymmetric correlation. An implementation for the quasi maximum likelihood estimator (QMLE) is provided. The proposed estimation method is applied to stock price data sets consisting of one financial system and four financial institutions: the US S&P 500 index, Bank of America Corporation, JP Morgan Chase & Co., Goldman Sachs Group, Inc. and Citigroup Inc. The data analysis shows that the proposed method has better in-sample and out-of-sample violation performance than existing methods and some other possible candidates.

Suggested Citation

  • Ji-Eun Choi & Dong Wan Shin, 2019. "Three regime bivariate normal distribution: a new estimation method for co-value-at-risk, CoVaR," The European Journal of Finance, Taylor & Francis Journals, vol. 25(18), pages 1817-1833, December.
    • Handle: RePEc:taf:eurjfi:v:25:y:2019:i:18:p:1817-1833
    DOI: 10.1080/1351847X.2019.1639208
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    Cited by:

    1. Fuchs Sebastian & Trutschnig Wolfgang, 2020. "On quantile based co-risk measures and their estimation," Dependence Modeling, De Gruyter, vol. 8(1), pages 396-416, January.
    2. Nurulkamal Masseran, 2021. "Modeling the Characteristics of Unhealthy Air Pollution Events: A Copula Approach," IJERPH, MDPI, vol. 18(16), pages 1-18, August.
    3. Ortega-Jiménez, P. & Sordo, M.A. & Suárez-Llorens, A., 2021. "Stochastic orders and multivariate measures of risk contagion," Insurance: Mathematics and Economics, Elsevier, vol. 96(C), pages 199-207.
    4. Fuchs Sebastian & Trutschnig Wolfgang, 2020. "On quantile based co-risk measures and their estimation," Dependence Modeling, De Gruyter, vol. 8(1), pages 396-416, January.

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