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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.

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Bibliographic Info

Paper provided by European Association of Agricultural Economists in its series 101st Seminar, July 5-6, 2007, Berlin Germany with number 9265.

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Date of creation: 2007
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Handle: RePEc:ags:eaa101:9265

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

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  1. Kenneth A. Froot, 2001. "The Market for Catastrophe Risk: A Clinical Examination," NBER Working Papers 8110, National Bureau of Economic Research, Inc.
  2. Härdle, Wolfgang Karl & Burnecki, Krzysztof & Weron, Rafał, 2004. "Simulation of risk processes," Papers 2004,01, Humboldt-Universität Berlin, Center for Applied Statistics and Economics (CASE).
  3. Krzysztof Burnecki & Grzegorz Kukla & Rafal Weron, 2000. "Property insurance loss distributions," HSC Research Reports HSC/00/03, Hugo Steinhaus Center, Wroclaw University of Technology.
  4. Burnecki, Krzysztof & Misiorek, Adam & Weron, Rafal, 2010. "Loss Distributions," MPRA Paper 22163, University Library of Munich, Germany.
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Cited by:
  1. 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.
  2. 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.
  3. 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.
  4. Joanne Ho & Martin Odening, 2009. "Weather-based estimation of wildfire risk," SFB 649 Discussion Papers SFB649DP2009-032, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  5. Nowak, Piotr & Romaniuk, Maciej, 2013. "Pricing and simulations of catastrophe bonds," Insurance: Mathematics and Economics, Elsevier, vol. 52(1), pages 18-28.

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