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Pricing of catastrophe insurance options written on a loss index with reestimation

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  • Biagini, Francesca
  • Bregman, Yuliya
  • Meyer-Brandis, Thilo

Abstract

We propose a valuation model for catastrophe insurance options written on a loss index. This kind of options distinguishes between a loss period [0,T1], during which the catastrophes may happen, and a development period [T1,T2], during which losses entered before T1 are reestimated. Here we suppose that the underlying loss index is given by a time inhomogeneous compound Poisson process before T1 and that losses are reestimated by a common factor given by an exponential time inhomogeneous Lévy process after T1. In this setting, using Fourier transform techniques, we are able to provide analytical pricing formulas for catastrophe options written on this kind of index.

Suggested Citation

  • Biagini, Francesca & Bregman, Yuliya & Meyer-Brandis, Thilo, 2008. "Pricing of catastrophe insurance options written on a loss index with reestimation," Insurance: Mathematics and Economics, Elsevier, vol. 43(2), pages 214-222, October.
    • Handle: RePEc:eee:insuma:v:43:y:2008:i:2:p:214-222
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    References listed on IDEAS

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    1. Christensen, Claus Vorm & Schmidli, Hanspeter, 2000. "Pricing catastrophe insurance products based on actually reported claims," Insurance: Mathematics and Economics, Elsevier, vol. 27(2), pages 189-200, October.
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    Cited by:

    1. Wang, Guanying & Wang, Xingchun & Shao, Xinjian, 2022. "Exchange options for catastrophe risk management," The North American Journal of Economics and Finance, Elsevier, vol. 59(C).
    2. Ernst Eberlein & Kathrin Glau & Antonis Papapantoleon, 2008. "Analysis of Fourier transform valuation formulas and applications," Papers 0809.3405, arXiv.org, revised Sep 2009.
    3. Eckhard Platen & David Taylor, 2016. "Loading Pricing of Catastrophe Bonds and Other Long-Dated, Insurance-Type Contracts," Papers 1610.09875, arXiv.org.
    4. Ben Ammar, Semir & Braun, Alexander & Eling, Martin, 2015. "Alternative Risk Transfer and Insurance-Linked Securities: Trends, Challenges and New Market Opportunities," I.VW HSG Schriftenreihe, University of St.Gallen, Institute of Insurance Economics (I.VW-HSG), volume 56, number 56.
    5. Thilini Mahanama & Abootaleb Shirvani & Svetlozar Rachev, 2022. "A Natural Disasters Index," Environmental Economics and Policy Studies, Springer;Society for Environmental Economics and Policy Studies - SEEPS, vol. 24(2), pages 263-284, April.
    6. Braun, Alexander, 2011. "Pricing catastrophe swaps: A contingent claims approach," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 520-536.
    7. Thilini V. Mahanama & Abootaleb Shirvani, 2020. "A Natural Disasters Index," Papers 2008.03672, arXiv.org.
    8. Bi, Hongwei & Wang, Guanying & Wang, Xingchun, 2019. "Valuation of catastrophe equity put options with correlated default risk and jump risk," Finance Research Letters, Elsevier, vol. 29(C), pages 323-329.
    9. Alessandro Ramponi, 2012. "Fourier Transform Methods For Regime-Switching Jump-Diffusions And The Pricing Of Forward Starting Options," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(05), pages 1-26.
    10. Wang, Xingchun, 2016. "Catastrophe equity put options with target variance," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 79-86.
    11. Wang, Xingchun, 2020. "Catastrophe equity put options with floating strike prices," The North American Journal of Economics and Finance, Elsevier, vol. 54(C).
    12. Wang, Xingchun, 2019. "Valuation of new-designed contracts for catastrophe risk management," The North American Journal of Economics and Finance, Elsevier, vol. 50(C).

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