Pricing Excess-of-loss Reinsurance Contracts Against Catastrophic Loss
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.
|Date of creation:||Jan 1998|
|Date of revision:|
|Contact details of provider:|| Postal: 3301 Steinberg Hall-Dietrich Hall, 3620 Locust Walk, Philadelphia, PA 19104.6367|
Web page: http://fic.wharton.upenn.edu/fic/
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- J. David Cummins & Hèlyette Geman, 1993. "An Asian Option to the Valuation of Insurance Futures Contracts," Center for Financial Institutions Working Papers 94-03, Wharton School Center for Financial Institutions, University of Pennsylvania.
- Gerber, Hans U., 1982. "On the numerical evaluation of the distribution of aggregate claims and its stop-loss premiums," Insurance: Mathematics and Economics, Elsevier, vol. 1(1), pages 13-18, January.
- Kenneth A. Froot & David S. Scharfstein & Jeremy C. Stein, 1994. "A Framework For Risk Management," Journal of Applied Corporate Finance, Morgan Stanley, vol. 7(3), pages 22-33.
- 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.
- Knut K. Aase, 1993. "A Jump/Diffusion Consumption-Based Capital Asset Pricing Model and the Equity Premium Puzzle," Mathematical Finance, Wiley Blackwell, vol. 3(2), pages 65-84.
- 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.
- 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.
- 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.
- 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.
- Merton, Robert C., 1975.
"Option pricing when underlying stock returns are discontinuous,"
787-75., Massachusetts Institute of Technology (MIT), Sloan School of Management.
- Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
- 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.
- Bühlmann, Hans, 1984. "The General Economic Premium Principle," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 14(01), pages 13-21, April.
- Heston, Steven L, 1993. " Invisible Parameters in Option Prices," Journal of Finance, American Finance Association, vol. 48(3), pages 933-47, July.
- Carolyn W. Chang, 1995. "A No-Arbitrage Martingale Analysis For Jump-Diffusion Valuation," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 18(3), pages 351-381, 09.
When requesting a correction, please mention this item's handle: RePEc:wop:pennin:98-09. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Thomas Krichel)
If references are entirely missing, you can add them using this form.