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An Asian Option to the Valuation of Insurance Futures Contracts

Listed author(s):
  • J. David Cummins
  • Hèlyette Geman

While insurers have a variety of instruments readily available to hedge the risk of assets and interest rate sensitive liabilities, until recently reinsurance was the only mechanism for hedging underwriting risk. The insurance futures contracts introduced in December 1992 by the Chicago Board of Trade (CBOT) offer insurers an alternative to reinsurance as a hedging device for under-writing risk. These instruments have the usual features of liquidity, anonymity, and low transaction costs that characterize futures contracts. Unlike reinsurance, hedging through futures has the advantage of reversibility since any position may be closed before the maturity of the futures contract if the overall exposure of the insurer has diminished. Reversing a reinsurance transaction exposes the insurer to relatively high transactions costs as well as additional charges to protect the reinsurer against adverse selection. Because futures contracts are based on losses incurred by a pool of a least 10 insurance companies selected by the Insurance Services Officer, the potential for adverse selection and the accompanying administrative costs are greatly diminished relative to a reinsurance contract. Unlike most futures contracts traded on the CBOT, insurance futures are based on an accumulation of insurance loss payments over a period of time rather than the price of a commodity or asset at the end of a period of time. The classical relationships between the spot price and the futures price do not hold. The fact that the futures price at maturity will reflect a sum of claim payments entails a structural similarity between this contract and an Asian option, for which the underlying asset is an average, i.e., a sum of spot prices (up to a multiplicative constant). Thus, it would be incorrect to price these instruments using standard futures pricing techniques. Geman and Yor (1992, 1993) investigate the exact solution of this problem. The authors apply the Geman-Yor approach to the valuation of the insurance catastrophe futures contracts offered by the CBOT. In their model, the state variable is assumed to be a geometric Brownian motion - the claims process. The payoff on the insurance futures contract is determined by the accumulation or integral of the state variable. The authors believe there is a significant systematic component to insurance losses, especially those involving catastrophes. Insurers should be able to reduce risk by trading futures contracts. In their view the primary reason for limited trading of insurance futures is the lack of information on the loss index. There is very little information to support parameter estimation or to assist traders in forming expectations. In the authors' view, the CBOT's current offerings are unlikely to be successful unless the information problem is solved.

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Paper provided by Wharton School Center for Financial Institutions, University of Pennsylvania in its series Center for Financial Institutions Working Papers with number 94-03.

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Date of creation: Sep 1993
Handle: RePEc:wop:pennin:94-03
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  1. Berger, Lawrence A & Cummins, J David & Tennyson, Sharon, 1992. "Reinsurance and the Liability Insurance Crisis," Journal of Risk and Uncertainty, Springer, vol. 5(3), pages 253-272, July.
  2. Shimko, David C., 1992. "The Valuation of Multiple Claim Insurance Contracts," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 27(02), pages 229-246, June.
  3. Kemna, A. G. Z. & Vorst, A. C. F., 1990. "A pricing method for options based on average asset values," Journal of Banking & Finance, Elsevier, vol. 14(1), pages 113-129, March.
  4. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
  5. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
  6. Stapleton, Richard C & Subrahmanyam, Marti G, 1984. " The Valuation of Multivariate Contingent Claims in Discrete Time Models," Journal of Finance, American Finance Association, vol. 39(1), pages 207-228, March.
  7. Brennan, M J, 1979. "The Pricing of Contingent Claims in Discrete Time Models," Journal of Finance, American Finance Association, vol. 34(1), pages 53-68, March.
  8. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
  9. 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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