IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i9p1363-d797065.html
   My bibliography  Save this article

Multiple-Trigger Catastrophe Bond Pricing Model and Its Simulation Using Numerical Methods

Author

Listed:
  • Riza Andrian Ibrahim

    (Master of Mathematics Study Program, Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Sumedang 45363, Indonesia)

  • Sukono

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

  • Herlina Napitupulu

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

Abstract

Investor interest in single-trigger catastrophe bonds (STCB) has the potential to decline in the future. It is triggered by the increasing trend of global catastrophe loss and intensity every year, which increases the probability that a claim of STCB will occur. To increase investor interest again, the issuance of multiple-trigger catastrophe bonds (MTCB) can be one solution. However, to issue MTCB, its pricing is more complex because it involves more factors than STCB. Therefore, this study aims to design a simple MTCB pricing model. The claim trigger indices used are actual loss and fatality. Then, a nonhomogeneous compound Poisson process is used to model actual losses and fatalities aggregate to consider catastrophe intensity. In addition, this study proposes numerical methods, namely the continuous distribution approximation method and the Nuel recursive method, to facilitate the application of the model. Finally, an analysis of the effect of catastrophe intensity and other factors on MTCB prices is also presented. This study is expected to help special-purpose vehicles as MTCB issuers in MTCB pricing.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:9:p:1363-:d:797065
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/9/1363/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/9/1363/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Vedenov, Dmitry V. & Epperson, James E. & Barnett, Barry J., 2006. "Designing Catastrophe Bonds to Securitize Systemic Risks in Agriculture: The Case of Georgia Cotton," Journal of Agricultural and Resource Economics, Western Agricultural Economics Association, vol. 31(2), pages 1-21, August.
    2. N. Karagiannis & H. Assa & A. A. Pantelous & C. G. Turvey, 2016. "Modelling and pricing of catastrophe risk bonds with a temperature-based agricultural application," Quantitative Finance, Taylor & Francis Journals, vol. 16(12), pages 1949-1959, December.
    3. 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.
    4. repec:fth:geneec:99.01 is not listed on IDEAS
    5. 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.
    6. 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.
    7. Henri Louberge & Evis Kellezi & Manfred Gilli, 1999. "Using Catastrophe-Linked Securities to Diversity Insurance Risk: A Financial Analysis of Cat Bonds," Journal of Insurance Issues, Western Risk and Insurance Association, vol. 22(2), pages 125-146.
    8. J. David Cummins & Mary A. Weiss, 2009. "Convergence of Insurance and Financial Markets: Hybrid and Securitized Risk‐Transfer Solutions," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 76(3), pages 493-545, September.
    9. Harrington, Scott E. & Niehaus, Greg, 2003. "Capital, corporate income taxes, and catastrophe insurance," Journal of Financial Intermediation, Elsevier, vol. 12(4), pages 365-389, October.
    10. Nadide Caglayan & Sule Itir Satoglu, 2021. "Multi-Objective Two-Stage Stochastic Programming Model for a Proposed Casualty Transportation System in Large-Scale Disasters: A Case Study," Mathematics, MDPI, vol. 9(4), pages 1-22, February.
    11. Chaubey, Yogendra P. & Garrido, Jose & Trudeau, Sonia, 1998. "On the computation of aggregate claims distributions: some new approximations," Insurance: Mathematics and Economics, Elsevier, vol. 23(3), pages 215-230, December.
    12. Anna Chernobai & Krzysztof Burnecki & Svetlozar Rachev & Stefan Trück & Rafał Weron, 2006. "Modelling catastrophe claims with left-truncated severity distributions," Computational Statistics, Springer, vol. 21(3), pages 537-555, December.
    13. Dickson,David C. M., 2005. "Insurance Risk and Ruin," Cambridge Books, Cambridge University Press, number 9780521846400.
    14. Jarrow, Robert A., 2010. "A simple robust model for Cat bond valuation," Finance Research Letters, Elsevier, vol. 7(2), pages 72-79, June.
    15. 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.
    16. 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.
    17. Zimbidis, Alexandros A. & Frangos, Nickolaos E. & Pantelous, Athanasios A., 2007. "Modeling Earthquake Risk via Extreme Value Theory and Pricing the Respective Catastrophe Bonds," ASTIN Bulletin, Cambridge University Press, vol. 37(1), pages 163-183, May.
    18. Dhaene, Jan, 1989. "Stochastic Interest Rates and Autoregressive Integrated Moving Average Processes," ASTIN Bulletin, Cambridge University Press, vol. 19(2), pages 131-138, November.
    19. 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.
    20. 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.
    21. 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.
    22. Xiaoyu Tan & Shenghong Li & Shuyi Wang, 2020. "Pricing European-Style Options in General Lévy Process with Stochastic Interest Rate," Mathematics, MDPI, vol. 8(5), pages 1-10, May.
    23. Wen Chao & Polinpapilinho Katina, 2021. "Valuing Multirisk Catastrophe Reinsurance Based on the Cox–Ingersoll–Ross (CIR) Model," Discrete Dynamics in Nature and Society, Hindawi, vol. 2021, pages 1-8, February.
    24. Thorsten Schmidt, 2014. "Catastrophe Insurance Modeled by Shot-Noise Processes," Risks, MDPI, vol. 2(1), pages 1-22, February.
    25. 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.
    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. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Jiayi Li & Zhiyan Cai & Yixuan Liu & Chengxiu Ling, 2022. "Extremal Analysis of Flooding Risk and Its Catastrophe Bond Pricing," Mathematics, MDPI, vol. 11(1), pages 1-14, December.
    2. 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.
    3. Yifan Tang & Conghua Wen & Chengxiu Ling & Yuqing Zhang, 2023. "Pricing Multi-Event-Triggered Catastrophe Bonds Based on a Copula–POT Model," Risks, MDPI, vol. 11(8), pages 1-19, August.
    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. 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. 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.
    7. Titi Purwandari & Riaman & Yuyun Hidayat & Sukono & Riza Andrian Ibrahim & Rizki Apriva Hidayana, 2023. "Selecting and Weighting Mechanisms in Stock Portfolio Design Based on Clustering Algorithm and Price Movement Analysis," Mathematics, MDPI, vol. 11(19), pages 1-22, October.
    8. 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.
    9. 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.
    10. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. Riza Andrian Ibrahim & Sukono & Herlina Napitupulu & Rose Irnawaty Ibrahim, 2024. "Earthquake Bond Pricing Model Involving the Inconstant Event Intensity and Maximum Strength," Mathematics, MDPI, vol. 12(6), pages 1-21, March.
    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. Eckhard Platen & David Taylor, 2016. "Loading Pricing of Catastrophe Bonds and Other Long-Dated, Insurance-Type Contracts," Research Paper Series 379, Quantitative Finance Research Centre, University of Technology, Sydney.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. Dixon Domfeh & Arpita Chatterjee & Matthew Dixon, 2022. "A Unified Bayesian Framework for Pricing Catastrophe Bond Derivatives," Papers 2205.04520, arXiv.org.
    15. Peter Carayannopoulos & Olga Kanj & M. Fabricio Perez, 2022. "Pricing dynamics in the market for catastrophe bonds," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 47(1), pages 172-202, January.
    16. 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.
    17. Chatoro, Marian & Mitra, Sovan & Pantelous, Athanasios A. & Shao, Jia, 2023. "Catastrophe bond pricing in the primary market: The issuer effect and pricing factors," International Review of Financial Analysis, Elsevier, vol. 85(C).
    18. Braun, Alexander, 2011. "Pricing catastrophe swaps: A contingent claims approach," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 520-536.
    19. Fabio Pizzutilo & Elisabetta Venezia, 2018. "Are catastrophe bonds effective financial instruments in the transport and infrastructure industries? Evidence from international financial markets," Business and Economic Horizons (BEH), Prague Development Center, vol. 14(2), pages 256-267, April.
    20. Apostolos Kiohos & Maria Paspati, 2021. "Alternative to Insurance Risk Transfer: Creating a catastrophe bond for Romanian earthquakes," Bulletin of Applied Economics, Risk Market Journals, vol. 8(1), pages 1-17.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:10:y:2022:i:9:p:1363-:d:797065. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.