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The influence of non-linear dependencies on the basis risk of industry loss warranties


  • Gatzert, Nadine
  • Kellner, Ralf


Index-linked catastrophic loss instruments represent an alternative to traditional reinsurance to hedge against catastrophic losses. The use of these instruments comes with benefits, such as a reduction of moral hazard and higher transparency. However, at the same time, it introduces basis risk as a crucial key risk factor, since the index and the company's losses are usually not fully dependent. The aim of this paper is to examine the impact of basis risk on an insurer's solvency situation when an industry loss warranty contract is used for hedging. Since previous literature has consistently stressed the importance of a high degree of dependence between the company's losses and the industry index, we extend previous studies by allowing for non-linear dependencies between relevant processes (high-risk and low-risk assets, insurance company's loss and industry index). The analysis shows that both the type and degree of dependence play a considerable role with regard to basis risk and solvency capital requirements and that other factors, such as relevant contract parameters of index-linked catastrophic loss instruments, should not be neglected to obtain a comprehensive and holistic view of their effect upon risk reduction.

Suggested Citation

  • Gatzert, Nadine & Kellner, Ralf, 2011. "The influence of non-linear dependencies on the basis risk of industry loss warranties," Insurance: Mathematics and Economics, Elsevier, vol. 49(1), pages 132-144, July.
  • Handle: RePEc:eee:insuma:v:49:y:2011:i:1:p:132-144

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    References listed on IDEAS

    1. J. David Cummins & Mary A. Weiss, 2009. "Convergence of Insurance and Financial Markets: Hybrid and Securitized Risk‐Transfer Solutions," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 76(3), pages 493-545, September.
    2. Burnecki, Krzysztof & Kukla, Grzegorz & Weron, Rafał, 2000. "Property insurance loss distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(1), pages 269-278.
    3. Zhou, Chen, 2010. "Dependence structure of risk factors and diversification effects," Insurance: Mathematics and Economics, Elsevier, vol. 46(3), pages 531-540, June.
    4. Lixin Zeng, 2005. "Enhancing reinsurance efficiency using index-based instruments," Journal of Risk Finance, Emerald Group Publishing, vol. 6(1), pages 6-16, January.
    5. Gatzert, Nadine & Schmeiser, Hato, 2008. "Combining fair pricing and capital requirements for non-life insurance companies," Journal of Banking & Finance, Elsevier, vol. 32(12), pages 2589-2596, December.
    6. Cummins, J. David & Lalonde, David & Phillips, Richard D., 2004. "The basis risk of catastrophic-loss index securities," Journal of Financial Economics, Elsevier, vol. 71(1), pages 77-111, January.
    7. Eling, Martin & Gatzert, Nadine & Schmeiser, Hato, 2009. "Minimum standards for investment performance: A new perspective on non-life insurer solvency," Insurance: Mathematics and Economics, Elsevier, vol. 45(1), pages 113-122, August.
    8. John Major, 1999. "Index Hedge Performance: Insurer Market Penetration and Basis Risk," NBER Chapters, in: The Financing of Catastrophe Risk, pages 391-432, National Bureau of Economic Research, Inc.
    9. Martin Eling & Denis Toplek, 2009. "Modeling and Management of Nonlinear Dependencies–Copulas in Dynamic Financial Analysis," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 76(3), pages 651-681, September.
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    Cited by:

    1. Kellner, Ralf & Gatzert, Nadine, 2013. "Estimating the basis risk of index-linked hedging strategies using multivariate extreme value theory," Journal of Banking & Finance, Elsevier, vol. 37(11), pages 4353-4367.
    2. Gatzert, Nadine & Kosub, Thomas, 2016. "Risks and risk management of renewable energy projects: The case of onshore and offshore wind parks," Renewable and Sustainable Energy Reviews, Elsevier, vol. 60(C), pages 982-998.


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