GAS Copula models on who’s systemically important in South Africa: Banks or Insurers?

  • Mathias Mandla Manguzvane
  • John Weirstrass Muteba MwambaEmail author


This paper makes use of the generalized autoregressive score (GAS) Copula model to estimate the Conditional Value at Risk (CoVaR) measure of systemic risk. The proposed measure of systemic risk considers the score of the conditional density as the main driver of time-varying dynamics of tail dependence among financial institutions. Not only does the GAS Copula-based CoVaR enable us to monitor the amount of systemic risk posed by different financial institutions at a specific date, it also allows for the forecasting of systemic risk over time. Our results based on a sample of daily equity returns collected from January 2000 to July 2017 surprisingly show that in South Africa, insurers are the most systemically risky compared to banks and other financial sectors. Moreover, we make use of flexible GAS Copulas in order to approximate complex dependence structures. To validate the robustness of our results over time, we divide our sample period into two sub samples, namely the pre-crisis period (January 2000 to June 2007) and the post-crisis period (January 2010 to July 2017). We obtain similar results in the pre-crisis period. However, in the post-crisis period banks are found to be the biggest threat to system-wide stability.


Banks Copula Generalized autoregressive score model Insurers South Africa Systemically important 

JEL Classification

C13 C58 G01 G21 G22 G28 



  1. Adams Z, Füss R, Gropp R (2011) Modelling spill over effects among financial institutions: a state dependent sensitivity value-at-risk approach. EBS Working PaperGoogle Scholar
  2. Adrian T, Brunnermeier MK (2016) CoVaR. Am Econ Rev 106(7):1705–1741CrossRefGoogle Scholar
  3. Bank for International Settlements (2009) Basel committee on banking supervision (BCBS). In: International convergence of capital measurement and capital standards: a revised frameworkGoogle Scholar
  4. Bernal O, Gnabo JY, Guilmin G (2014) Assessing the contribution of banks, insurance and other financial services to systemic risk. J Bank Financ 47(1):270–287CrossRefGoogle Scholar
  5. Claessens S, Herring R, Schoenmaker D, Summe K (2010) A safer world financial system: improving the resolution of systemic institutions. Geneva Reports on the World EconomyGoogle Scholar
  6. Creal D, Koopman SJ, Lucas A (2013) Generalized autoregressive score models with applications. J Appl Econ 28(5):777–795CrossRefGoogle Scholar
  7. Cummins JD, Weiss MA (2013) Systemic risk and the insurance industry. Handbook of insurance. Springer, New York, pp 745–793CrossRefGoogle Scholar
  8. Eckernkemper T (2018) Modelling systemic risk: time-varying tail dependence when forecasting marginal expected shortfall. J Financ Econom 16(1):63–117CrossRefGoogle Scholar
  9. Financial Stability Board (2010) Reducing the moral hazard posed by systemically important financial institutions. Financial stability board report, 20 October 2010Google Scholar
  10. Girardi G, Ergün AT (2013) Systemic risk measurement: multivariate GARCH estimation of CoVaR. J Bank Financ 37(8):3169–3180CrossRefGoogle Scholar
  11. Hu L (2006) Dependence patterns across financial markets: a mixed Copula approach. Appl Financ Econom 16(10):717–729CrossRefGoogle Scholar
  12. Huang X, Zhou H, Zhu H (2009) A framework for assessing the systemic risk of major financial institutions. J Bank Financ 33(11):2036–2049CrossRefGoogle Scholar
  13. International Monetary Fund, Financial Stability Board, Bank for International Settlements (2011) Macroprudential policy tools and frameworks–update to G20 Finance Ministers and Central Bank GovernorsGoogle Scholar
  14. Jordanger LA, Tjøstheim D (2014) Model selection of copulas: AIC versus a cross validation copula information criterion. Stat Probab Lett 92:249–255CrossRefGoogle Scholar
  15. Koopman SJ, Lucas A (2008) A non-Gaussian panel time series model for estimating and decomposing default risk. J Bus Econom Stat 26(4):510–525CrossRefGoogle Scholar
  16. Laeven L, Ratnovski L, Tong H (2016) Bank size, capital, and systemic risk: some international evidence. J Bank Financ 69(1):25–34CrossRefGoogle Scholar
  17. Lorenzoni G (2008) Inefficient credit booms. Rev Econ Stud 75(3):809–833CrossRefGoogle Scholar
  18. Mainik G, Schaanning E (2014) On dependence consistency of CoVaR and some other systemic risk measures. Stat Risk Model 31(1):49–77Google Scholar
  19. Makatjane K, Xaba D, Moroke N (2017) Application of generalized autoregressive score model to stock returns. Int J Econ Manag Eng 11(11):2714–2717Google Scholar
  20. Manguzvane M, Muteba Mwamba JW (2017) Modelling systemic risk in the South African banking sector using CoVaR, ERSA Working Paper (No. 709)Google Scholar
  21. Nelson DB (1991) Conditional heteroskedasticity in asset returns: a new approach. Econom J Econom Soc 59:347–370Google Scholar
  22. Patton AJ (2006) Modelling asymmetric exchange rate dependence. Int Econ Rev 47(2):527–556CrossRefGoogle Scholar
  23. Reboredo JC, Ugolini A (2015) Systemic risk in European sovereign debt markets: a CoVaR-Copula approach. J Int Money Financ 51:214–244CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of EconomicsUniversity of JohannesburgJohannesburgSouth Africa

Personalised recommendations