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Application of Compound Poisson Process in Pricing Catastrophe Bonds: A Systematic Literature Review

Author

Listed:
  • Sukono

    (Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Jatinangor 45363, Indonesia)

  • Hafizan Juahir

    (East Coast Environmental Research Institute (ESERI), Universiti Sultan Zainal Abidin, Kuala Terengganu 21300, Malaysia)

  • Riza Andrian Ibrahim

    (Doctoral Program, Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Jatinangor 45363, Indonesia)

  • Moch Panji Agung Saputra

    (Doctoral Program, Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Jatinangor 45363, Indonesia)

  • Yuyun Hidayat

    (Department of Statistics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Bandung 45363, Indonesia)

  • Igif Gimin Prihanto

    (Research Center for Testing Technology and Standards, National Research and Innovation Agency, Jakarta Pusat 10340, Indonesia)

Abstract

The compound Poisson process (CPP) is often used in catastrophe risk modeling, for example, aggregate loss risk modeling. Hence, CPP can be involved in pricing catastrophe bonds (CAT bonds) because it requires a catastrophe risk modeling method. However, studies of how the application of CPP in pricing CAT bonds is still scarce. Therefore, this study aims to conduct a systematic literature review (SLR) on how CPP is used in pricing CAT bonds. The SLR consists of three stages: the literature selection, bibliometric analysis, and gap analysis. At the literature selection stage, the 30 articles regarding the application of CPP in pricing CAT bonds are obtained. Then, the conceptual and nonconceptual structures of the articles are mapped at the bibliometric analysis stage. Finally, in the gap analysis stage, the application of CPP in pricing CAT bonds from the previous studies is analyzed, and new research opportunities are studied. This research can be a reference for researchers regarding the application of CPP in pricing CAT bonds and can motivate them to design more beneficial ways of pricing CAT bonds with CPP in the future.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:15:p:2668-:d:874767
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    References listed on IDEAS

    as
    1. Nowak, Piotr & Romaniuk, Maciej, 2013. "Pricing and simulations of catastrophe bonds," Insurance: Mathematics and Economics, Elsevier, vol. 52(1), pages 18-28.
    2. Jian Liu & Jihong Xiao & Lizhao Yan & Fenghua Wen, 2014. "Valuing Catastrophe Bonds Involving Credit Risks," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-6, April.
    3. Wolfgang Karl Härdle & Brenda López Cabrera, 2010. "Calibrating CAT Bonds for Mexican Earthquakes," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 77(3), pages 625-650, September.
    4. Giuricich, Mario Nicoló & Burnecki, Krzysztof, 2019. "Modelling of left-truncated heavy-tailed data with application to catastrophe bond pricing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 498-513.
    5. Egami, Masahiko & Young, Virginia R., 2008. "Indifference prices of structured catastrophe (CAT) bonds," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 771-778, April.
    6. Frédéric Godin & Van Son Lai & Denis-Alexandre Trottier, 2019. "A general class of distortion operators for pricing contingent claims with applications to CAT bonds," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2019(7), pages 558-584, August.
    7. Lee, Jin-Ping & Yu, Min-Teh, 2007. "Valuation of catastrophe reinsurance with catastrophe bonds," Insurance: Mathematics and Economics, Elsevier, vol. 41(2), pages 264-278, September.
    8. Nick Georgiopoulos, 2017. "Pricing catastrophe bonds with multistage stochastic programming," Computational Management Science, Springer, vol. 14(3), pages 297-312, July.
    9. Junfei Chen & Guiyun Liu & Liu Yang & Quanxi Shao & Huimin Wang, 2013. "Pricing and Simulation for Extreme Flood Catastrophe Bonds," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 27(10), pages 3713-3725, August.
    10. Riza Andrian Ibrahim & Sukono & Herlina Napitupulu, 2022. "Multiple-Trigger Catastrophe Bond Pricing Model and Its Simulation Using Numerical Methods," Mathematics, MDPI, vol. 10(9), pages 1-17, April.
    11. Wen Chao & Huiwen Zou, 2018. "Multiple-Event Catastrophe Bond Pricing Based on CIR-Copula-POT Model," Discrete Dynamics in Nature and Society, Hindawi, vol. 2018, pages 1-9, June.
    12. Froot, Kenneth A., 2001. "The market for catastrophe risk: a clinical examination," Journal of Financial Economics, Elsevier, vol. 60(2-3), pages 529-571, May.
    13. Jin-Chuan, Duan & Moreau, Arthur F. & Sealey, C. W., 1995. "Deposit insurance and bank interest rate risk: Pricing and regulatory implications," Journal of Banking & Finance, Elsevier, vol. 19(6), pages 1091-1108, September.
    14. Joanne Linnerooth-Bayer & Aniello Amendola, 2000. "Global Change, Natural Disasters and Loss-sharing: Issues of Efficiency and Equity," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 25(2), pages 203-219, April.
    15. Guoqu Deng & Shiqiang Liu & Li Li & Chushi Deng, 2020. "Research on the Pricing of Global Drought Catastrophe Bonds," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-7, May.
    16. Samuel Cox & Hal Pedersen, 2000. "Catastrophe Risk Bonds," North American Actuarial Journal, Taylor & Francis Journals, vol. 4(4), pages 56-82.
    17. 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.
    18. Victor Vaugirard, 2004. "A canonical first passage time model to pricing nature-linked bonds," Economics Bulletin, AccessEcon, vol. 7(2), pages 1-7.
    19. Thorsten Schmidt, 2014. "Catastrophe Insurance Modeled by Shot-Noise Processes," Risks, MDPI, vol. 2(1), pages 1-22, February.
    20. Vaugirard, Victor E., 2003. "Pricing catastrophe bonds by an arbitrage approach," The Quarterly Review of Economics and Finance, Elsevier, vol. 43(1), pages 119-132.
    21. Beer, Simone & Braun, Alexander, 2022. "Market-consistent valuation of natural catastrophe risk," Journal of Banking & Finance, Elsevier, vol. 134(C).
    22. Xiaoli Zhang & Cary Chi-Liang Tsai, 2018. "The Optimal Write-Down Coefficients in a Percentage for a Catastrophe Bond," North American Actuarial Journal, Taylor & Francis Journals, vol. 22(1), pages 1-21, January.
    23. Wolfgang Karl Härdle & Brenda López Cabrera, 2010. "Calibrating CAT Bonds for Mexican Earthquakes," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 77(3), pages 625-650, September.
    24. Ole Ellegaard & Johan A. Wallin, 2015. "The bibliometric analysis of scholarly production: How great is the impact?," Scientometrics, Springer;Akadémiai Kiadó, vol. 105(3), pages 1809-1831, December.
    25. repec:ebl:ecbull:v:7:y:2004:i:2:p:1-7 is not listed on IDEAS
    26. J. David Cummins, 2008. "CAT Bonds and Other Risk‐Linked Securities: State of the Market and Recent Developments," Risk Management and Insurance Review, American Risk and Insurance Association, vol. 11(1), pages 23-47, March.
    27. Jerry R. Skees & Barry J. Barnett & Anne G. Murphy, 2008. "Creating insurance markets for natural disaster risk in lower income countries: the potential role for securitization," Agricultural Finance Review, Emerald Group Publishing Limited, vol. 68(1), pages 151-167, May.
    28. Lai, Van Son & Parcollet, Mathieu & Lamond, Bernard F., 2014. "The valuation of catastrophe bonds with exposure to currency exchange risk," International Review of Financial Analysis, Elsevier, vol. 33(C), pages 243-252.
    29. Zonggang Ma & Chaoqun Ma & Shisong Xiao, 2017. "Pricing Zero-Coupon Catastrophe Bonds Using EVT with Doubly Stochastic Poisson Arrivals," Discrete Dynamics in Nature and Society, Hindawi, vol. 2017, pages 1-14, September.
    30. Jarrow, Robert A., 2010. "A simple robust model for Cat bond valuation," Finance Research Letters, Elsevier, vol. 7(2), pages 72-79, June.
    31. 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.
    32. Tang, Qihe & Yuan, Zhongyi, 2019. "Cat Bond Pricing Under A Product Probability Measure With Pot Risk Characterization," ASTIN Bulletin, Cambridge University Press, vol. 49(2), pages 457-490, May.
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    Cited by:

    1. Wulan Anggraeni & Sudradjat Supian & Sukono & Nurfadhlina Binti Abdul Halim, 2022. "Earthquake Catastrophe Bond Pricing Using Extreme Value Theory: A Mini-Review Approach," Mathematics, MDPI, vol. 10(22), pages 1-22, November.
    2. Wulan Anggraeni & Sudradjat Supian & Sukono & Nurfadhlina Abdul Halim, 2023. "Single Earthquake Bond Pricing Framework with Double Trigger Parameters Based on Multi Regional Seismic Information," Mathematics, MDPI, vol. 11(3), pages 1-44, January.
    3. Wulan Anggraeni & Sudradjat Supian & Sukono & Nurfadhlina Abdul Halim, 2023. "Catastrophe Bond Diversification Strategy Using Probabilistic–Possibilistic Bijective Transformation and Credibility Measures in Fuzzy Environment," Mathematics, MDPI, vol. 11(16), pages 1-30, August.
    4. 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.
    5. Sukono & Herlina Napitupulu & Riaman & Riza Andrian Ibrahim & Muhamad Deni Johansyah & Rizki Apriva Hidayana, 2023. "A Regional Catastrophe Bond Pricing Model and Its Application in Indonesia’s Provinces," Mathematics, MDPI, vol. 11(18), pages 1-20, September.
    6. Sukono & Riza Andrian Ibrahim & Moch Panji Agung Saputra & Yuyun Hidayat & Hafizan Juahir & Igif Gimin Prihanto & Nurfadhlina Binti Abdul Halim, 2022. "Modeling Multiple-Event Catastrophe Bond Prices Involving the Trigger Event Correlation, Interest, and Inflation Rates," Mathematics, MDPI, vol. 10(24), pages 1-18, December.

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