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An Equilibrium Model of Catastrophe Insurance Futures and Spreads

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  • Knut Aase

    (Norwegian School of Economics and Business Administration, Helleveien 30, N-5035 Bergen-Sandviken, and the University of Oslo, Norway)

Abstract

This article presents a valuation model of futures contracts and derivatives on such contracts, when the underlying delivery value is an insurance index, which follows a stochastic process containing jumps of random claim sizes at random time points of accident occurrence. Applications are made on insurance futures and spreads, a relatively new class of instruments for risk management launched by the Chicago Board of Trade in 1993, anticipated to start in Europe and perhaps also in other parts of the world in the future. The article treats the problem of pricing catastrophe risk, which is priced in the model and not treated as unsystematic risk. Several closed pricing formulas are derived, both for futures contracts and for futures derivatives, such as caps, call options, and spreads. The framework is that of partial equilibrium theory under uncertainty. The Geneva Papers on Risk and Insurance Theory (1999) 24, 69–96. doi:10.1023/A:1008785300001

Suggested Citation

  • Knut Aase, 1999. "An Equilibrium Model of Catastrophe Insurance Futures and Spreads," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 24(1), pages 69-96, June.
    • Handle: RePEc:pal:genrir:v:24:y:1999:i:1:p:69-96
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    Citations

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    Cited by:

    1. Aase, Knut K, 2005. "Using Option Pricing Theory to Infer About Historical Equity Premiums," University of California at Los Angeles, Anderson Graduate School of Management qt3dd602j5, Anderson Graduate School of Management, UCLA.
    2. Aase, Knut K, 2005. "The perpetual American put option for jump-diffusions with applications," University of California at Los Angeles, Anderson Graduate School of Management qt31g898nz, Anderson Graduate School of Management, UCLA.
    3. Aase, Knut K., 2004. "The perpetual American put option for jump-diffusions: Implications for equity premiums," Discussion Papers 2004/19, Norwegian School of Economics, Department of Business and Management Science.
    4. Thies R. Popp & Wiebke Nowack, 2020. "Resilience through the Financialisation of Risks? The Case of a Dairy System in Northwest Germany," Sustainability, MDPI, vol. 12(15), pages 1-20, August.
    5. Chang, Carolyn W. & Chang, Jack S.K. & Lu, WeLi, 2010. "Pricing catastrophe options with stochastic claim arrival intensity in claim time," Journal of Banking & Finance, Elsevier, vol. 34(1), pages 24-32, January.
    6. Geman, Helyette & Yor, Marc, 1997. "Stochastic time changes in catastrophe option pricing," Insurance: Mathematics and Economics, Elsevier, vol. 21(3), pages 185-193, December.
    7. Eckhard Platen & David Taylor, 2016. "Loading Pricing of Catastrophe Bonds and Other Long-Dated, Insurance-Type Contracts," Papers 1610.09875, arXiv.org.
    8. Truong, Chi & Trück, Stefan, 2016. "It’s not now or never: Implications of investment timing and risk aversion on climate adaptation to extreme events," European Journal of Operational Research, Elsevier, vol. 253(3), pages 856-868.
    9. Oleg Kolesnikov & Alexander Markov & Daulet Smagulov & Sergejs Solovjovs, 2019. "Cyber bonds and their pricing models," Papers 1911.06698, arXiv.org.
    10. Nick Georgiopoulos, 2017. "Pricing catastrophe bonds with multistage stochastic programming," Computational Management Science, Springer, vol. 14(3), pages 297-312, July.
    11. Mathieu Gatumel & Dominique Guegan, 2008. "Towards an understanding approach of the insurance linked securities market," Post-Print halshs-00235354, HAL.
    12. Chang, Carolyn W. & Chang, Jack S.K. & Lu, WeiLi, 2008. "Pricing catastrophe options in discrete operational time," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 422-430, December.
    13. Pérez-Fructuoso, María José, 2017. "Tarificación de bonos sobre catástrofes (cat bonds) con desencadenantes de índices de pérdidas. Modelación mediante un proceso de Ornstein-Uhlenbeck || Pricing Loss Index Triggered Cat Bonds. An Ornst," Revista de Métodos Cuantitativos para la Economía y la Empresa = Journal of Quantitative Methods for Economics and Business Administration, Universidad Pablo de Olavide, Department of Quantitative Methods for Economics and Business Administration, vol. 24(1), pages 340-361, Diciembre.
    14. Knut K. Aase, 2004. "A Pricing Model for Quantity Contracts," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 71(4), pages 617-642, December.
    15. Muermann, Alexander, 2002. "Pricing catastrophe insurance derivatives," LSE Research Online Documents on Economics 24904, London School of Economics and Political Science, LSE Library.
    16. Ma, Zong-Gang & Ma, Chao-Qun, 2013. "Pricing catastrophe risk bonds: A mixed approximation method," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 243-254.
    17. Alexander Muermann, 2002. "Pricing Catastrophe Insurance Derivatives," FMG Discussion Papers dp400, Financial Markets Group.
    18. de Lange, Petter E. & Fleten, Stein-Erik & Gaivoronski, Alexei A., 2004. "Modeling financial reinsurance in the casualty insurance business via stochastic programming," Journal of Economic Dynamics and Control, Elsevier, vol. 28(5), pages 991-1012, February.
    19. Schmeck, Maren Diane & Schmidli, Hanspeter, 2019. "Mortality Options: the Point of View of an Insurer," Center for Mathematical Economics Working Papers 616, Center for Mathematical Economics, Bielefeld University.
    20. Blanchet-Scalliet, Christophette & El Karoui, Nicole & Martellini, Lionel, 2005. "Dynamic asset pricing theory with uncertain time-horizon," Journal of Economic Dynamics and Control, Elsevier, vol. 29(10), pages 1737-1764, October.
    21. Zhu, Wenge, 2017. "Wanting robustness in insurance: A model of catastrophe risk pricing and its empirical test," Insurance: Mathematics and Economics, Elsevier, vol. 77(C), pages 14-23.
    22. Aase, Knut K., 2005. "Using Option Pricing Theory to Infer About Equity Premiums," Discussion Papers 2005/11, Norwegian School of Economics, Department of Business and Management Science.
    23. Braun, Alexander, 2011. "Pricing catastrophe swaps: A contingent claims approach," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 520-536.
    24. Schmeck, Maren Diane & Schmidli, Hanspeter, 2021. "Mortality options: The point of view of an insurer," Insurance: Mathematics and Economics, Elsevier, vol. 96(C), pages 98-115.
    25. Paul Embrechts, 1996. "Actuarial versus Financial Pricing of Insurance," Center for Financial Institutions Working Papers 96-17, Wharton School Center for Financial Institutions, University of Pennsylvania.

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