An Asian Option to the Valuation of Insurance Futures Contracts
J. David Cummins
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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