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Earthquake Catastrophe Bond Pricing Using Extreme Value Theory: A Mini-Review Approach

Author

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  • Wulan Anggraeni

    (Doctoral Program of Mathematics, Faculty of Mathematics and Natural Science, Universitas Padjadjaran, Sumedang 45363, Indonesia)

  • Sudradjat Supian

    (Departemen of Mathematics, Faculty of Mathematics and Natural Science, Universitas Padjadjaran, Sumedang 45363, Indonesia)

  • Sukono

    (Departemen of Mathematics, Faculty of Mathematics and Natural Science, Universitas Padjadjaran, Sumedang 45363, Indonesia)

  • Nurfadhlina Binti Abdul Halim

    (Faculty of Science and Technology, University Sains Islam Malaysia, Bandar Baru Nilai, Nilai 71800, Negeri Sembilan, Malaysia)

Abstract

Earthquake catastrophe bond pricing models (ECBPMs) employ extreme value theory (EVT) to predict severe losses, although studies on EVT’s use in ECBPMs are still rare. Therefore, this study aimed to use a mini-review approach (MRA) to examine the use of EVT and identify the gaps and weaknesses in the methods or models developed. The MRA stages include planning, search and selection, analysis, and interpretation of the results. The selection results showed five articles regarding the application of EVT in ECBPMs. Furthermore, the analysis found the following: First, the generalized extreme value (GEV) could eliminate extreme data in a period. Second, the trigger model using two parameters is better than one, but the study did not discuss the joint distribution of the two parameters. Third, the autoregressive integrated moving average (ARIMA) allows negative values. Fourth, Cox–Ingersoll–Ross (CIR) in-coupon modeling is less effective in depicting the real picture. This is because it has a constant volatility assumption and cannot describe jumps due to monetary policy. Based on these limitations, it is hoped that future studies can develop an ECBPM that reduces the moral hazard.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:22:p:4196-:d:968052
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    References listed on IDEAS

    as
    1. Chen, Hua & Cummins, J. David, 2010. "Longevity bond premiums: The extreme value approach and risk cubic pricing," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 150-161, February.
    2. Donthu, Naveen & Kumar, Satish & Mukherjee, Debmalya & Pandey, Nitesh & Lim, Weng Marc, 2021. "How to conduct a bibliometric analysis: An overview and guidelines," Journal of Business Research, Elsevier, vol. 133(C), pages 285-296.
    3. Stupfler, Gilles & Yang, Fan, 2018. "Analyzing And Predicting Cat Bond Premiums: A Financial Loss Premium Principle And Extreme Value Modeling," ASTIN Bulletin, Cambridge University Press, vol. 48(1), pages 375-411, January.
    4. 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.
    5. 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.
    6. 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.
    7. Morteza Tavanaie Marvi & Daniël Linders, 2021. "Decomposition of Natural Catastrophe Risks: Insurability Using Parametric CAT Bonds," Risks, MDPI, vol. 9(12), pages 1-19, December.
    8. 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.
    9. 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.
    10. Rika Amelia & Nursanti Anggriani & Asep K. Supriatna & Noor Istifadah, 2022. "Mathematical Model for Analyzing the Dynamics of Tungro Virus Disease in Rice: A Systematic Literature Review," Mathematics, MDPI, vol. 10(16), pages 1-18, August.
    11. Mohammad Ansari Esfeh & H. Jithamala Caldera & Seiran Heshami & Nadia Moshahedi & Sumedha Chandana Wirasinghe, 2016. "The severity of earthquake events -- statistical analysis and classification," International Journal of Urban Sciences, Taylor & Francis Journals, vol. 20(sup1), pages 4-24, July.
    12. Maochao Xu & Yiying Zhang, 2021. "Data Breach CAT Bonds: Modeling and Pricing," North American Actuarial Journal, Taylor & Francis Journals, vol. 25(4), pages 543-561, November.
    13. Marc Gürtler & Martin Hibbeln & Christine Winkelvos, 2016. "The Impact of the Financial Crisis and Natural Catastrophes on CAT Bonds," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 83(3), pages 579-612, September.
    14. Cummins, J. David & Lalonde, David & Phillips, Richard D., 2004. "The basis risk of catastrophic-loss index securities," Journal of Financial Economics, Elsevier, vol. 71(1), pages 77-111, January.
    15. 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.
    16. 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.
    17. 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.
    18. Bahl, Raj Kumari & Sabanis, Sotirios, 2021. "Model-independent price bounds for Catastrophic Mortality Bonds," Insurance: Mathematics and Economics, Elsevier, vol. 96(C), pages 276-291.
    19. Silke Finken & Christian Laux, 2009. "Catastrophe Bonds and Reinsurance: The Competitive Effect of Information‐Insensitive Triggers," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 76(3), pages 579-605, September.
    20. 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.
    21. 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.
    22. 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.
    23. Samuel Cox & Hal Pedersen, 2000. "Catastrophe Risk Bonds," North American Actuarial Journal, Taylor & Francis Journals, vol. 4(4), pages 56-82.
    24. 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.
    25. Giuseppe Orlando & Rosa Maria Mininni & Michele Bufalo, 2019. "Interest rates calibration with a CIR model," Journal of Risk Finance, Emerald Group Publishing Limited, vol. 20(4), pages 370-387, September.
    26. Cyrielle Dollet & Philippe Guéguen, 2022. "Global occurrence models for human and economic losses due to earthquakes (1967–2018) considering exposed GDP and population," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 110(1), pages 349-372, January.
    27. Pizzutilo, Fabio & Venezia, Elisabetta, 2018. "Are catastrophe bonds effective financial instruments in the transport and infrastructure industries? Evidence and review from international financial markets," Business and Economic Horizons (BEH), Prague Development Center (PRADEC), vol. 14(2), February.
    28. Li Long & Shansuo Zheng & Yixin Zhang & Longfei Sun & Yan Zhou & Liguo Dong, 2020. "CEDLES: a framework for plugin-based applications for earthquake risk prediction and loss assessment," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 103(1), pages 531-556, August.
    29. 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.
    30. 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.
    31. Sanubari Tansah Tresna & Subiyanto & Sudradjat Supian, 2022. "Mathematical Models for Typhoid Disease Transmission: A Systematic Literature Review," Mathematics, MDPI, vol. 10(14), pages 1-12, July.
    32. Peng, Qidi & Schellhorn, Henry, 2018. "On the distribution of extended CIR model," Statistics & Probability Letters, Elsevier, vol. 142(C), pages 23-29.
    33. N. Zhang & H. Huang, 2018. "Assessment of world disaster severity processed by Gaussian blur based on large historical data: casualties as an evaluating indicator," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 92(1), pages 173-187, May.
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    Cited by:

    1. 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.
    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. 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.
    4. 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.
    5. 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.
    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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