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Calibrating CAT bonds for Mexican earthquakes

Author

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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
    DOI: 10.22004/ag.econ.9265
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    References listed on IDEAS

    as
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    More about this item

    Keywords

    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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