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

Author

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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.
    2. repec:spr:compst:v:51:y:2000:i:3:p:357-374 is not listed on IDEAS
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    Cited by:

    1. Ernst Eberlein & Kathrin Glau & Antonis Papapantoleon, 2008. "Analysis of Fourier transform valuation formulas and applications," Papers 0809.3405, arXiv.org, revised Sep 2009.
    2. Eckhard Platen & David Taylor, 2016. "Loading Pricing of Catastrophe Bonds and Other Long-Dated, Insurance-Type Contracts," Papers 1610.09875, arXiv.org.
    3. Braun, Alexander, 2011. "Pricing catastrophe swaps: A contingent claims approach," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 520-536.
    4. Wang, Xingchun, 2016. "Catastrophe equity put options with target variance," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 79-86.

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