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Pricing of Reinsurance Contracts in the Presence of Catastrophe Bonds

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  • Haslip, Gareth G.
  • Kaishev, Vladimir K.

Abstract

A methodology for pricing of reinsurance contracts in the presence of a catastrophe bond is developed. An important advantage of this approach is that it allows for the pricing of reinsurance contracts consistent with the observed market prices of catastrophe bonds on the same underlying risk process. Within the proposed methodology, an appropriate financial pricing formula is derived, under a market implied risk neutral probability measure for both a catastrophe bond and an aggregate excess of loss reinsurance contract, using a generalised Fourier transform. Efficient numerical methods for the evaluation of this formula, such as the Fast Fourier transform and Fractional Fast Fourier transform, are considered. The methodology is illustrated on several examples including Pareto and Gamma claim severities.

Suggested Citation

  • Haslip, Gareth G. & Kaishev, Vladimir K., 2010. "Pricing of Reinsurance Contracts in the Presence of Catastrophe Bonds," ASTIN Bulletin, Cambridge University Press, vol. 40(1), pages 307-329, May.
    • Handle: RePEc:cup:astinb:v:40:y:2010:i:01:p:307-329_00
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    Cited by:

    1. Spyridon M. Tzaninis & Nikolaos D. Macheras, 2020. "A characterization of progressively equivalent probability measures preserving the structure of a compound mixed renewal process," Papers 2007.05289, arXiv.org, revised Jul 2020.
    2. Beer, Simone & Braun, Alexander, 2022. "Market-consistent valuation of natural catastrophe risk," Journal of Banking & Finance, Elsevier, vol. 134(C).
    3. Burnecki, Krzysztof & Giuricich, Mario Nicoló & Palmowski, Zbigniew, 2019. "Valuation of contingent convertible catastrophe bonds — The case for equity conversion," Insurance: Mathematics and Economics, Elsevier, vol. 88(C), pages 238-254.
    4. Sukono & Hafizan Juahir & Riza Andrian Ibrahim & Moch Panji Agung Saputra & Yuyun Hidayat & Igif Gimin Prihanto, 2022. "Application of Compound Poisson Process in Pricing Catastrophe Bonds: A Systematic Literature Review," Mathematics, MDPI, vol. 10(15), pages 1-19, July.
    5. Denis-Alexandre Trottier & Van Son Lai, 2017. "Reinsurance or CAT Bond? How to Optimally Combine Both," Working Papers 2017-003, Department of Research, Ipag Business School.

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