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Valuing clustering in catastrophe derivatives

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  • Sebastian Jaimungal
  • Yuxiang Chong

Abstract

The role that clustering in activity and/or severity plays in catastrophe modeling and derivative valuation is a key aspect that has been overlooked in the recent literature. Here, we propose two marked point processes to account for these features. The first approach assumes the points are driven by a stochastic hazard rate modulated by a Markov chain while marks are drawn from a regime-specific distribution. In the second approach, the points are driven by a self-exciting process while marks are drawn from an independent distribution. Within this context, we provide a unified approach to efficiently value catastrophe options--such as those embedded in catastrophe bonds--and show that our results are within the 95% confidence interval computed using Monte Carlo simulations. Our approach is based on deriving the valuation PIDE and utilizes transforms to provide semi-analytical closed-form solutions. This contrasts with most prior works where the valuation formulae require computing several infinite sums together with numerical integration.

Suggested Citation

  • Sebastian Jaimungal & Yuxiang Chong, 2014. "Valuing clustering in catastrophe derivatives," Quantitative Finance, Taylor & Francis Journals, vol. 14(2), pages 259-270, February.
    • Handle: RePEc:taf:quantf:v:14:y:2014:i:2:p:259-270
    DOI: 10.1080/14697688.2013.799775
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    Cited by:

    1. Gunther Leobacher & Philip Ngare, 2014. "Utility indifference pricing of derivatives written on industrial loss indexes," Papers 1404.0879, arXiv.org.
    2. Shao, Jia & Papaioannou, Apostolos D. & Pantelous, Athanasios A., 2017. "Pricing and simulating catastrophe risk bonds in a Markov-dependent environment," Applied Mathematics and Computation, Elsevier, vol. 309(C), pages 68-84.
    3. Eckhard Platen & David Taylor, 2016. "Loading Pricing of Catastrophe Bonds and Other Long-Dated, Insurance-Type Contracts," Papers 1610.09875, arXiv.org.
    4. Colaneri, Katia & Frey, Rüdiger, 2021. "Classical solutions of the backward PIDE for Markov modulated marked point processes and applications to CAT bonds," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 498-507.
    5. Krzysztof Burnecki & Mario Nicoló Giuricich, 2017. "Stable Weak Approximation at Work in Index-Linked Catastrophe Bond Pricing," Risks, MDPI, vol. 5(4), pages 1-19, December.
    6. Riza Andrian Ibrahim & Sukono & Herlina Napitupulu & Rose Irnawaty Ibrahim, 2023. "How to Price Catastrophe Bonds for Sustainable Earthquake Funding? A Systematic Review of the Pricing Framework," Sustainability, MDPI, vol. 15(9), pages 1-19, May.

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