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Pricing Excess-of-loss Reinsurance Contracts Against Catastrophic Loss

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  • J. David Cummins
  • Christopher M. Lewis
  • Richard D. Phillips

Abstract

This paper develops a pricing methodology and pricing estimates for the proposed Federal excess-of- loss (XOL) catastrophe reinsurance contracts. The contracts, proposed by the Clinton Administration, would provide per-occurrence excess-of-loss reinsurance coverage to private insurers and reinsurers, where both the coverage layer and the fixed payout of the contract are based on insurance industry losses, not company losses. In financial terms, the Federal government would be selling earthquake and hurricane catastrophe call options to the insurance industry to cover catastrophic losses in a loss layer above that currently available in the private reinsurance market. The contracts would be sold annually at auction, with a reservation price designed to avoid a government subsidy and ensure that the program would be self supporting in expected value. If a loss were to occur that resulted in payouts in excess of the premiums collected under the policies, the Federal government would use its ability to borrow at the risk-free rate to fund the losses. During periods when the accumulated premiums paid into the program exceed the losses paid, the buyers of the contracts implicitly would be lending money to the Treasury, reducing the costs of government debt. The expected interest on these "loans" offsets the expected financing (borrowing) costs of the program as long as the contracts are priced appropriately. By accessing the Federal government's superior ability to diversify risk inter-temporally, the contracts could be sold at a rate lower than would be required in conventional reinsurance markets, which would potentially require a high cost of capital due to the possibility that a major catastrophe could bankrupt some reinsurers. By pricing the contacts at least to break even, the program would provide for eventual private-market "crowding out" through catastrophe derivatives and other innovative catastrophic risk financing mechanisms. We develop prices for the contracts using two samples of catastrophe losses: (1) historical catastrophic loss experience over the period 1949-1994 as reported by Property Claim Services; and (2) simulated catastrophe losses based on an engineering simulation analysis conducted by Risk Management Solutions. We used maximum likelihood estimation techniques to fit frequency and severity probability distributions to the catastrophic loss data, and then used the distributions to estimate expected losses under the contracts. The reservation price would be determined by adding an administrative expense charge and a risk premium to the expected losses for the specified layer of coverage. We estimate the expected loss component of the government's reservation price for proposed XOL contracts covering the entire U.S., California, Florida, and the Southeast. We used a loss layer of $25-50 billion for illustrative purposes.

Suggested Citation

  • J. David Cummins & Christopher M. Lewis & Richard D. Phillips, 1998. "Pricing Excess-of-loss Reinsurance Contracts Against Catastrophic Loss," Center for Financial Institutions Working Papers 98-09, Wharton School Center for Financial Institutions, University of Pennsylvania.
  • Handle: RePEc:wop:pennin:98-09
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    References listed on IDEAS

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    Cited by:

    1. Torben Andersen, 2001. "Managing Economic Exposures of Natural Disasters: Exploring Alternative Financial Risk Management Opportunities and Instruments," IDB Publications (Working Papers) 8934, Inter-American Development Bank.
    2. Massimo Mariani & Paola Amoruso, 2016. "The Effectiveness of Catastrophe Bonds in Portfolio Diversification," International Journal of Economics and Financial Issues, Econjournals, vol. 6(4), pages 1760-1767.
    3. J. David Cummins & Michael Suher & George Zanjani, 1975. "Federal Financial Exposure to Natural Catastrophe Risk," NBER Chapters,in: Measuring and Managing Federal Financial Risk, pages 61-92 National Bureau of Economic Research, Inc.
    4. Prof. Dr. Walter Krämer & Sebastian Schich, "undated". "Large - scaledisasters and the insurance industry," Working Papers 4, Business and Social Statistics Department, Technische Universität Dortmund, revised Mar 2005.
    5. Cummins, J. David & McDonald, James B. & Merrill, Craig, 2007. "Risky Loss Distributions and Modeling the Loss Reserve Pay-out Tail," Review of Applied Economics, Lincoln University, Department of Financial and Business Systems, vol. 0(Number 1-), pages 1-23.
    6. A. K. Bahl & O. Baltzer & A. Rau-Chaplin & B. Varghese & A. Whiteway, 2013. "Achieving Speedup in Aggregate Risk Analysis using Multiple GPUs," Papers 1308.2572, arXiv.org.
    7. J. David Cummins & Christopher M. Lewis, 2002. "Catastrophic Events, Parameter Uncertainty and the Breakdown of Implicit Long-term Contracting in the Insurance Market: The Case of Terrorism Insurance," Center for Financial Institutions Working Papers 02-40, Wharton School Center for Financial Institutions, University of Pennsylvania.
    8. M. Martin Boyer & Charles M. Nyce, 2011. "An Industrial Organization Theory of Risk Sharing," CIRANO Working Papers 2011s-78, CIRANO.
    9. Marc Atlan & Hélyette Geman & Dilip Madan & Marc Yor, 2007. "Correlation and the pricing of risks," Annals of Finance, Springer, vol. 3(4), pages 411-453, October.
    10. Cummins, J David & Mahul, Olivier, 2003. "Optimal Insurance with Divergent Beliefs about Insurer Total Default Risk," Journal of Risk and Uncertainty, Springer, vol. 27(2), pages 121-138, October.
    11. James F. Moore, 1999. "Tail Estimation and Catastrophe Security Pricing: Can We Tell What Target We Hit if We Are Shooting in the Dark?," Center for Financial Institutions Working Papers 99-14, Wharton School Center for Financial Institutions, University of Pennsylvania.
    12. Epperson, James E., 2008. "Securitizing peanut production risk with catastrophe (CAT) bonds," Faculty Series 44512, University of Georgia, Department of Agricultural and Applied Economics.
    13. Dong, A.X.D. & Chan, J.S.K., 2013. "Bayesian analysis of loss reserving using dynamic models with generalized beta distribution," Insurance: Mathematics and Economics, Elsevier, vol. 53(2), pages 355-365.
    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. Froot, Kenneth A. & O'Connell, Paul G.J., 2008. "On the pricing of intermediated risks: Theory and application to catastrophe reinsurance," Journal of Banking & Finance, Elsevier, vol. 32(1), pages 69-85, January.
    16. J. M. Kim & P. K. Woods & Y. J. Park & K. Son, 2016. "Estimating the Texas Windstorm Insurance Association claim payout of commercial buildings from Hurricane Ike," 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. 84(1), pages 405-424, October.
    17. Cummins, J. David & Doherty, Neil & Lo, Anita, 2002. "Can insurers pay for the "big one"? Measuring the capacity of the insurance market to respond to catastrophic losses," Journal of Banking & Finance, Elsevier, vol. 26(2-3), pages 557-583, March.
    18. David M. Cutler & Richard J. Zeckhauser, 1999. "Reinsurance for Catastrophes and Cataclysms," NBER Chapters,in: The Financing of Catastrophe Risk, pages 233-274 National Bureau of Economic Research, Inc.
    19. Lin, Shih-Kuei & Chang, Chia-Chien & Powers, Michael R., 2009. "The valuation of contingent capital with catastrophe risks," Insurance: Mathematics and Economics, Elsevier, vol. 45(1), pages 65-73, August.
    20. Kent Smetters, 2005. "Insuring Against Terrorism: The Policy Challenge," NBER Working Papers 11038, National Bureau of Economic Research, Inc.
    21. Abdel-Raheem F. Fares & Eid Ahmad Abou-Bakr, 2012. "Economics of Insurance against Natural Catastrophes: Over-Burdened Arab Insurers," Review of Economics & Finance, Better Advances Press, Canada, vol. 2, pages 95-105, August.

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