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

Ji Eun Choi, Dong Wan Shin

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


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.

Original languageEnglish
Pages (from-to)1817-1833
Number of pages17
JournalEuropean Journal of Finance
Issue number18
StatePublished - 12 Dec 2019

Bibliographical note

Funding Information:
This work was supported by the National Research Foundation of Korea [2019R1A2C1004679].

Publisher Copyright:
© 2019, © 2019 Informa UK Limited, trading as Taylor & Francis Group.


  • Asymmetric correlation
  • contagion
  • CoVaR
  • delta-CoVaR
  • quasi maximum likelihood
  • systemic risk


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