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Calibrating CAT bonds for Mexican earthquakes

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  • Haerdle, Wolfgang
  • Cabrera, Brenda Lopez

Abstract

The study of natural catastrophe models plays an important role in the prevention and mitigation of disasters. After the occurrence of a natural disaster, the reconstruction can be financed with catastrophe bonds (CAT bonds) or reinsurance. This paper examines the calibration of a real parametric CAT bond for earthquakes that was sponsored by the Mexican government. The calibration of the CAT bond is based on the estimation of the intensity rate that describes the earthquake process from the two sides of the contract, the reinsurance and the capital markets, and from the historical data. The results demonstrate that, under specific conditions, the financial strategy of the government, a mix of reinsurance and CAT bond, is optimal in the sense that it provides coverage of USD 450 million for a lower cost than the reinsurance itself. Since other variables can affect the value of the losses caused by earthquakes, e.g. magnitude, depth, city impact, etc., we also derive the price of a hypothetical modeled-index loss (zero) coupon CAT bond for earthquakes, which is based on the compound doubly stochastic Poisson pricing methodology from BARYSHNIKOV, MAYO and TAYLOR (2001) and BURNECKI and KUKLA (2003). In essence, this hybrid trigger combines modeled loss and index trigger types, trying to reduce basis risk borne by the sponsor while still preserving a nonindemnity trigger mechanism. Our results indicate that the (zero) coupon CAT bond price increases as the threshold level increases, but decreases as the expiration time increases. Due to the quality of the data, the results show that the expected loss is considerably more important for the valuation of the CAT bond than the entire distribution of losses. The study of natural catastrophe models plays an important role in the prevention and mitigation of disasters. After the occurrence of a natural disaster, the reconstruction can be financed with catastrophe bonds (CAT bonds) or reinsurance. This paper examines the calibration of a real parametric CAT bond for earthquakes that was sponsored by the Mexican government. The calibration of the CAT bond is based on the estimation of the intensity rate that describes the earthquake process from the two sides of the contract, the reinsurance and the capital markets, and from the historical data. The results demonstrate that, under specific conditions, the financial strategy of the government, a mix of reinsurance and CAT bond, is optimal in the sense that it provides coverage of USD 450 million for a lower cost than the reinsurance itself. Since other variables can affect the value of the losses caused by earthquakes, e.g. magnitude, depth, city impact, etc., we also derive the price of a hypothetical modeled-index loss (zero) coupon CAT bond for earthquakes, which is based on the compound doubly stochastic Poisson pricing methodology from BARYSHNIKOV, MAYO and TAYLOR (2001) and BURNECKI and KUKLA (2003). In essence, this hybrid trigger combines modeled loss and index trigger types, trying to reduce basis risk borne by the sponsor while still preserving a nonindemnity trigger mechanism. Our results indicate that the (zero) coupon CAT bond price increases as the threshold level increases, but decreases as the expiration time increases. Due to the quality of the data, the results show that the expected loss is considerably more important for the valuation of the CAT bond than the entire distribution of losses.

Suggested Citation

  • Haerdle, Wolfgang & Cabrera, Brenda Lopez, 2007. "Calibrating CAT bonds for Mexican earthquakes," 101st Seminar, July 5-6, 2007, Berlin Germany 9265, European Association of Agricultural Economists.
  • Handle: RePEc:ags:eaa101:9265
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    References listed on IDEAS

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    1. 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.
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    6. 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.
    7. Robert W. Klein & Shaun Wang, 2009. "Catastrophe Risk Financing in the United States and the European Union: A Comparative Analysis of Alternative Regulatory Approaches," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 76(3), pages 607-637.
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    1. repec:eee:apmaco:v:309:y:2017:i:c:p:68-84 is not listed on IDEAS
    2. Borensztein, Eduardo & Cavallo, Eduardo & Jeanne, Olivier, 2017. "The welfare gains from macro-insurance against natural disasters," Journal of Development Economics, Elsevier, vol. 124(C), pages 142-156.
    3. Alexis Louaas & Pierre Picard, 2014. "Optimal Insurance For Catastrophic Risk: Theory And Application To Nuclear Corporate Liability," Working Papers hal-01097897, HAL.
    4. Volodymyr Perederiy, 2007. "Kombinierte Liquiditäts- und Solvenzkennzahlen und ein darauf basierendes Insolvenzprognosemodell für deutsche GmbHs," SFB 649 Discussion Papers SFB649DP2007-060, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    5. Lo, Chien-Ling & Lee, Jin-Ping & Yu, Min-Teh, 2013. "Valuation of insurers’ contingent capital with counterparty risk and price endogeneity," Journal of Banking & Finance, Elsevier, vol. 37(12), pages 5025-5035.
    6. 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.
    7. Joanne Ho & Martin Odening, 2009. "Weather-based estimation of wildfire risk," SFB 649 Discussion Papers SFB649DP2009-032, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    8. Nowak, Piotr & Romaniuk, Maciej, 2013. "Pricing and simulations of catastrophe bonds," Insurance: Mathematics and Economics, Elsevier, vol. 52(1), pages 18-28.
    9. Braun, Alexander, 2011. "Pricing catastrophe swaps: A contingent claims approach," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 520-536.
    10. Truong, Chi & Trück, Stefan, 2016. "It’s not now or never: Implications of investment timing and risk aversion on climate adaptation to extreme events," European Journal of Operational Research, Elsevier, vol. 253(3), pages 856-868.
    11. repec:gam:jrisks:v:5:y:2017:i:4:p:64-:d:123183 is not listed on IDEAS
    12. Têtu Alexandre & Lai Van Son & Soumaré Issouf & Gendron Michel, 2015. "Hedging Flood Losses Using Cat Bonds," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 9(2), pages 149-184, July.

    More about this item

    Keywords

    CAT bonds; Reinsurance; Earthquakes; Doubly Stochastic Poisson Process; Trigger mechanism; Risk and Uncertainty;

    JEL classification:

    • G19 - Financial Economics - - General Financial Markets - - - Other
    • G29 - Financial Economics - - Financial Institutions and Services - - - Other
    • N26 - Economic History - - Financial Markets and Institutions - - - Latin America; Caribbean
    • N56 - Economic History - - Agriculture, Natural Resources, Environment and Extractive Industries - - - Latin America; Caribbean
    • Q29 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Renewable Resources and Conservation - - - Other
    • Q54 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - Climate; Natural Disasters and their Management; Global Warming

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