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Studies in Nonlinear Dynamics & Econometrics

Ed. by Mizrach, Bruce

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Volume 24 (2020)

Dependence Modelling in Insurance via Copulas with Skewed Generalised Hyperbolic Marginals

Vitali Alexeev
  • Finance Discipline Group, UTS Business School, University of Technology Sydney, Sydney, NSW 2007, Australia
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Katja Ignatieva
  • Corresponding author
  • School of Risk and Actuarial Studies, Business School, UNSW Australia, Sydney, NSW 2052, Australia
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Thusitha Liyanage
  • Portfolio and Market Risk Management Department, Commonwealth Bank of Australia, Sydney, NSW 2000, Australia
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2019-12-20 | DOI: https://doi.org/10.1515/snde-2018-0094


This paper investigates dependence among insurance claims arising from different lines of business (LoBs). Using bivariate and multivariate portfolios of losses from different LoBs, we analyse the ability of various copulas in conjunction with skewed generalised hyperbolic (GH) marginals to capture the dependence structure between individual insurance risks forming an aggregate risk of the loss portfolio. The general form skewed GH distribution is shown to provide the best fit to univariate loss data. When modelling dependency between LoBs using one-parameter and mixture copula models, we favour models that are capable of generating upper tail dependence, that is, when several LoBs have a strong tendency to exhibit extreme losses simultaneously. We compare the selected models in their ability to quantify risks of multivariate portfolios. By performing an extensive investigation of the in- and out-of-sample Value-at-Risk (VaR) forecasts by analysing VaR exceptions (i.e. observations of realised portfolio value that are greater than the estimated VaR), we demonstrate that the selected models allow to reliably quantify portfolio risk. Our results provide valuable insights with regards to the nature of dependence and fulfils one of the primary objectives of the general insurance providers aiming at assessing total risk of an aggregate portfolio of losses when LoBs are correlated.

Keywords: copula; dependence modelling; insurance losses; skewed generalised hyperbolic distribution

JEL Classification: G22; C46; C15


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About the article

aThe opinions expressed in this article are the author’s own and do not reflect the view of the Commonwealth Bank of Australia.

Published Online: 2019-12-20

Citation Information: Studies in Nonlinear Dynamics & Econometrics, 20180094, ISSN (Online) 1558-3708, DOI: https://doi.org/10.1515/snde-2018-0094.

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