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Pricing Excess-of-Loss Reinsurance Contracts against Cat as trophic Loss

In: The Financing of Catastrophe Risk

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  • David Cummins
  • Christopher Lewis
  • Richard 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 pri

(This abstract was borrowed from another version of this item.)

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Bibliographic Info

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This chapter was published in:

  • Kenneth A. Froot, 1999. "The Financing of Catastrophe Risk," NBER Books, National Bureau of Economic Research, Inc, number froo99-1, October.
    This item is provided by National Bureau of Economic Research, Inc in its series NBER Chapters with number 7949.

    Handle: RePEc:nbr:nberch:7949

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    References

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    1. Cummins, J. David & Dionne, Georges & McDonald, James B. & Pritchett, B. Michael, 1990. "Applications of the GB2 family of distributions in modeling insurance loss processes," Insurance: Mathematics and Economics, Elsevier, vol. 9(4), pages 257-272, December.
    2. Merton, Robert C., 1975. "Option pricing when underlying stock returns are discontinuous," Working papers 787-75., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    3. Heston, Steven L, 1993. " Invisible Parameters in Option Prices," Journal of Finance, American Finance Association, vol. 48(3), pages 933-47, July.
    4. Naik, Vasanttilak & Lee, Moon, 1990. "General Equilibrium Pricing of Options on the Market Portfolio with Discontinuous Returns," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 493-521.
    5. Chang, Carolyn W, 1995. "A No-Arbitrage Martingale Analysis for Jump-Diffusion Valuation," Journal of Financial Research, Southern Finance Association & Southwestern Finance Association, vol. 18(3), pages 351-81, Fall.
    6. Mayers, David & Smith, Clifford W, Jr, 1982. "On the Corporate Demand for Insurance," The Journal of Business, University of Chicago Press, vol. 55(2), pages 281-96, April.
    7. Cummins, J. David & Grace, Elizabeth, 1994. "Tax management and investment strategies of property-liability insurers," Journal of Banking & Finance, Elsevier, vol. 18(1), pages 43-72, January.
    8. Mayers, David & Smith, Clifford W, Jr, 1990. "On the Corporate Demand for Insurance: Evidence from the Reinsurance Market," The Journal of Business, University of Chicago Press, vol. 63(1), pages 19-40, January.
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    Citations

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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 8934, Inter-American Development Bank.
    2. 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.
    3. Walter Kraemer & Sebastian Schich, 2008. "Large-Scale Disasters and the Insurance Industry," CESifo Working Paper Series 2243, CESifo Group Munich.
    4. Martin Nell & Andreas Richter, 2000. "Catastrophe Index-Linked Securities and Reinsurance as Substituties," Working Paper Series: Finance and Accounting 56, Department of Finance, Goethe University Frankfurt am Main.
    5. 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.
    6. M. Martin Boyer & Charles M. Nyce, 2011. "An Industrial Organization Theory of Risk Sharing," CIRANO Working Papers 2011s-78, CIRANO.
    7. 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.
    8. Torben Andersen, 2002. "Innovative Financial Instruments for Natural Disaster Risk Management," IDB Publications 30738, Inter-American Development Bank.
    9. 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.
    10. Epperson, James E., 2008. "Securitizing peanut production risk with catastrophe (CAT) bonds," Faculty Series 44512, University of Georgia, Department of Agricultural and Applied Economics.
    11. 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.
    12. Kenneth A. Froot & Paul G. J. O'Connell, 1997. "On The Pricing of Intermediated Risks: Theory and Application to Catastrophe Reinsurance," NBER Working Papers 6011, National Bureau of Economic Research, Inc.
    13. 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.
    14. David M. Cutler & Richard J. Zeckhauser, 1997. "Reinsurance for Catastrophes and Cataclysms," NBER Working Papers 5913, National Bureau of Economic Research, Inc.
    15. 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.
    16. Kent Smetters, 2005. "Insuring Against Terrorism: The Policy Challenge," NBER Working Papers 11038, National Bureau of Economic Research, Inc.

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