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Dependencies and systemic risk in the European insurance sector: New evidence based on Copula-DCC-GARCH model and selected clustering methods



Objective: The objective of this article is to study the correlations between the most important European insurers and their participation in systemic risk in the insurance sector. We compare systemic risk in different market regimes.

Research Design & Methods: We use statistical clustering methods for time units (weeks) to which we assign conditional variances obtained from the estimated Copula- Dynamic Conditional Correlations-Generalised Auto-Regressive Conditional Heteroskedasticity model (C-DCC-GARCH). In each of the identified market regimes we determine the Conditional Value at Risk CoVaR systemic risk measure.

Findings: In this article we show a positive correlation of all the insurance companies under consideration. During global market crises the correlation appears stronger than in ‘normal times.’ This confirms that the insurance sector generates systemic risk in the presence of turbulences on financial markets, since the value level of the compared index CoVar is much higher in these conditions.

Implications & Recommendations: Our research confirms the insurance sector’s contribution to Systemic Risk. Thus, it is important to develop an analysis of systemic risk with a particular attention to the evolution of risk in time and the institutions' interconnectedness in the context of contagion using also some new modelling tools.

Contribution & Value Added: A novel approach of this article is the analysis of dependencies in the insurance sector using the C-DCC-GARCH model with taxonomic methods.


systemic risk; insurance market; Copula-DCC-GARCH(C-DCC-GARCH)

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Author Biography

Anna Denkowska

College of Economics, Finance and Law, Department of Mathematics, Assistant Professor (PhD)

Stanisław Wanat

College of Economics, Finance and Law, Department of Mathematics, Associate Professor (PhD, habilitation).


  1. Acharya, V.V., Pedersen, L.H., Philippon, T., & Richardson, M.P. (2010). Measuring Systemic Risk, SSRN Electronic Journal.
  2. Baluch, F., Mutenga, S., & Parsons, C. (2011). Insurance, Systemic Risk and the Financial Crisis. The Geneva Papers on Risk and Insurance – Issues and Practice, 36(1), 126-163. 10.1057/gpp.2010.40.
  3. Barrieu, P., & Scandolo, G. (2014). Assessing financial model risk. European Journal of Operational Research, 1-30.
  4. Baur, P., Enz, R., & Zanetti, A. (2003). Reinsurance—A Systemic Risk?. Zürich: Swiss.
  5. Bell, M., & Keller, B. (2009). Insurance and Stability: The Reform of Insurance Regulation (Zurich Financial Services Group Working Paper). Zurich, Switzerland Bernanke.
  6. Berdin, E., & Sottocornola, M. (2015). Assessing Systemic Risk of the European Insurance Industry. Financial Stability Report, EIOPA, 57-75.
  7. Bernal, O., Gnabo, J.-Y., & Guilmin, G. (2014). Assessing the contribution of banks, insurance and other financial services to systemic risk. Journal of Banking & Finance, 47, 270-287.
  8. Bernardi, M., & Catania, L. (2015). Switching GAS Copula Models for Systemic Risk Assess-ment.arXiv:1504.03733v1 [stat.ME]
  9. Bierth, C., Irresberger, F., & Weiß, G.N.F. (2015). Systemic risk of insurers around the globe. Jour-nal of Banking & Finance, 55, 232-245. 10.1016/j.jbankfin.2015.02.014
  10. Billio, M., Getmansky, M., Lo, A.W., & Pelizzon, L. (2012). Econometric measures of connectedness and systemic risk in the finance and insurance sectors. Journal of Financial Economics, 104(3), 535-559.
  11. Box, G.E.P., & Jenkins, G.M. (1970). Time Series Analysis: Forecasting and Control. San Francisco: Holden-Day.
  12. Brechmann, C., Hendrich, K., & Czado, C. (2013). Conditional copula simulation for systemic risk stress testing. Insurance: Mathematics and Economics,53(3), 722-732.
  13. Calinski, T., & Harabasz, J. (1974). A dendrite method for cluster analysis. Communications in Statistics, 3(1), 1-27.
  14. Chen, H., Cummins, J.D., Viswanathan, K.S., & Weiss, M.A. (2013). Systemic Risk and the Intercon-nectedness Between Banks and Insurers: An Econometric Analysis. Journal of Risk and Insur-ance, 81(3), 623-652.
  15. Cummins, J.D., & Weiss, M.A. (2014a; 2014b). Systemic Risk and The U.S. Insurance Sector. Jour-nal of Risk and Insurance, 81(3), 489-527.
  16. Czerwińska, T. (2014). Systemic risk in the insurance sector, Problemy Zarządzania, 12(48), 41-63.
  17. Denkowska, A., & Wanat, S. (2020). A Tail Dependence-Based MST and Their Topological Indica-tors in Modeling Systemic Risk in the European Insurance Sector. Risks, 8(2), 1-22.
  18. Di Bernardino, E., Fernández-Ponce, J.M., Palacios-Rodríguez, F., & Rodríguez-Griñolo, M.R. (2015). On multivariate extensions of the conditional Value-at-Risk measure. Insurance: Mathematics and Economics, 61, 1-16.
  19. Di Clemente, A. (2018). Estimating the marginal contribution to systemic risk by a CoVar-model based on copula functions and extreme value theory. Economic Notes by Banca Monte dei Paschi di Siena SpA, 47(1), 69-112.
  20. Dungey, M., Luciani, M., & Veredas, D. (2014). The Emergence of Systemically Important Insurers. CIFR paper, 038, September.
  21. Dunn, C.J. (1974) Well-separated clusters and optimal fuzzy partitions. Journal of Cybernetics, 4, 95-104.
  22. EIOPA (2017). Systemic risk and macroprudential policy in insurance. Luxembourg: Publication Office of the European Union.
  23. Eling, M., & Pankoke, D. (2014). Systemic risk in the insurance sector – what do we know. Working Papers on management and risk insurance, University of St Gallen.
  24. Engle, R.F. (2002). Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models. Journal of Business and Economic Sta-tistics, 20(3), 339-350.
  25. European Systemic Risk Board. (2015, December). Report on systemic risks in the EU insurance sector.
  26. Fiszeder, P. (2009). Modele klasy GARCH w empirycznych badaniach finansowych. Toruń: Wydaw-nictwo Naukowe Uniwersytetu Mikołaja Kopernika.
  27. Gajzler, M. (2019). Wykorzystanie bazującego na kopuli modelu delta CoVaR do analizy ryzyka systemowego na europejskim rynku ubezpieczeń. In A. Prędki (Ed.), Zastosowania narzędzi analitycznych w ekonomii, finansach i zarządzaniu (pp. 119-129). Kraków: Uniwersytet Eko-nomiczny w Krakowie.
  28. Geneva Association. (2010). Systemic risk in insurance: an analysis of insurance and financial stability. Technical report, Special Report of The Geneva Association Systemic Risk Working Group, Switzerland.
  29. Ghalanos, A. (2019). Multivariate GARCH Models. Package ‘rmgarch’. CRAN Packages Retrieved from on January 2020.
  30. Grace, M.F. (2011). The Insurance Industry and Systemic Risk: Evidence and Discussion.Working Paper, Georgia State University.
  31. Harrington, S.E. (2009). The Financial Crisis, Systemic Risk, and the Future of Insurance Regula-tion. Journal of Risk and Insurance, 76(4), 785-819.
  32. Hair, J. (1997). Multivariate models and dependence concepts. London: Chapman-Hall.
  33. IAIS. (2011). Insurance and financial stability.
  34. Jobst, A.A. (2014). Systemic Risk in the Insurance Sector: A Review of Current Assessment Ap-proaches.The Geneva Papers on Risk and Insurance – Issues and Practice, 39(3), 440-470.
  35. Kanno, M. (2016). The network structure and systemic risk in the global non-life insurance market. Insurance: Mathematics and Economics, 67, 38-53.
  36. Karimalis, E.N., & Nomikos, N.K. (2018). Measuring systemic risk in the European banking sector: a copula CoVar approach. The European Journal of Finance, 24(11), 944-975.
  37. Kaufman, L., & Rousseeuw, P.J. (1990). Finding Groups in Data: An Introduction to Cluster Analysis. New York: Wiley &Sons.
  38. Kessler, D. (2013). Why (Re)insurance is Not Systemic. Journal of Risk and Insurance, 81, (3), 477-488.
  39. van Lelyveld, I., Liedorp, F., & Kampman, M. (2011). An Empirical Assessment of Reinsurance Risk. Journal of Financial Stability, 7(4), 191-203.
  40. Mühlnickel J., & Weiß, G.N.F. (2014). Why do some insurers become systemically rele-vant?.Journal of Financial Stability, 13, 95-117.
  41. Mühlnickel, J., & Weiß, G.N.F. (2015). Consolidation and systemic risk in the international insur-ance industry. Journal of Financial Stability 18, 187-202.
  42. Nelson, D.B. (1991). Conditional Heteroskedasticity in Asset Returns: A New Approach. Economet-rica, 59, 347-370.
  43. Oh, D.H., & Patton, A.J. (2018). Time-varying systemic risk: evidence from a dynamic copula model of CDS spreads. Journal of Business and Economic Statistics, 36(2), 181-195.
  44. Patton, A.J. (2006). Modelling asymmetric exchange rate. International Economic Review. 47, 527-556.
  45. Radice, M.P. (2010). Systemische Risiken im Versicherungssektor?. FINMA Working Paper.
  46. Reboredo, J.C., & Ugolini, A. (2015). Systemic risk in European sovereign debt markets: A CoVaR-copula approach. Journal of International Money and Finance, 51, 214-244.
  47. Schwarcz, D., & Schwarcz, S.L. (2014). Regulating Systemic Risk in Insurance. 81 University of Chicago Law Review, 1569-1640.
  48. Tang, Q., & Yang, F. (2012). On the Haezendonck–Goovaerts risk measure for extreme risks. Insur-ance: Mathematics and Economics, 50(1), 217-227.
  49. Wanat, S., Śmiech, S., & Papież, M. (2016). In Serch of Hedges and Safe Havens in Global Finan-cial Markets. Statistics in Transition. New Series, 17(3), 557-574.
  50. Xie, X., & Beni, G. (1991). Validity measure for fuzzy clustering. IEEE Transactions on Pattern Anal-ysis and Machine Intelligence, 13, 841-847.


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