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... long call position combined with a short call position with a higher exercise price) as opposed to futures contracts because option spreads have payoffs similar to catastrophe reinsurance contracts (=-=Cummins and Geman 1994-=-; 1995); (2) the lack of historical data on the underlying indices (D’Arcy and France 1992); and (3) the basis risk associated with broad geographical indices. The CBOT discontinued the futures contra...

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...ttlement value for the CAT-futures is FT2 = 25 000 × min(IT2 , 2), where IT2 is the ISO-index at the end of the reporting period, i.e. the ratio between the losses incurred during the event quarter and reported up till 3 months later and the premium volume for the companies participating in the pool. Example 1.1. The June contract covers losses from events occurring in April, May and June and are reported to the participating companies by the end of September. The June contract expires on 5 January, the following year. The contract is illustrated in Fig. 1. 1.2. The CAT-future pricing problem Cummins and Geman (1993) were the first to price the insurance futures. Their approach was quite different from the approach used in this paper. As model they used integrated geometric Brownian motion. This allowed them to apply techniques arising from pricing Asian options. The model, however, seems to be far from reality. At times where a catastrophe occurs or shortly thereafter, one would expect a strong increase of the loss index. It therefore is preferable to use a marked point process as it is popular in actuarial mathematics. The price to pay for the more realistic model is “non-uniqueness” of the market; see ...

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... to Bühlmann [6], Gerber [13], and Grandell [15] for the latter. In a sequence of papers, Brennan and Schwartz [5], Bacinello and Ortu [2], Bacinello and Persson [3], and Nielsen and Sandmann [21] investigate the pricing of equity-linked life insurance contracts. The benefits of these insurance policies depend on the performance of a reference portfolio that is traded on the capital market. These contracts thus belong to a market containing insurance contracts that are based on both capital market and insurance related risk in form of policyholders’ mortality risk. Aase [1], Cummins and Geman [7], and Embrechts and Meister [10] examine the valuation of financial contracts that are based on natural catastrophic risk and that were traded at the Chicago Board of Trade (CBoT). The market modeled in these papers consists of financial contracts based on insurance related risk. 2 In two articles by Delbaen and Haezendonck [8] and Sondermann [23] the authors show how premium calculation principles for reinsurance contracts can be embedded in a no-arbitrage framework. The important contribution of these papers lies in the construction of an analytical bridge between actuarial and financial val...

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...oth problems are inherently related to the fact that price processes of insurance derivatives cannot be uniquely determined solely on the basis of excluding arbitrage opportunities. Cummins and Geman =-=[9]-=- were the first to investigate the valuation of catastrophe futures and derivative on futures. These securities were the first generation of traded contracts at the Chicago Board of Trade. The authors...