Academic journal article Journal of Risk and Insurance

Pricing Catastrophe Insurance Futures Call Spreads: A Randomized Operational Time Approach

Academic journal article Journal of Risk and Insurance

Pricing Catastrophe Insurance Futures Call Spreads: A Randomized Operational Time Approach

Article excerpt

INTRODUCTION

Amid much fanfare, the Chicago Board of Trade (CBOT) launched catastrophe insurance futures contracts (CAT futures) in 1992 and catastrophe insurance futures call spreads (CAT spreads) in 1993, with contract values linked to the loss ratios compiled by the Insurance Services Office (ISO). The CBOT replaced the ISO loss ratios by new loss ratios compiled by Property Claims Services (PCS) in September 1995. These derivative contracts provide underwriters and risk managers an effective alternative to hedge and trade systematic catastrophic losses. Insurers traditionally seek protection against underwriting risk through the mechanism of reinsurance. Because of worldwide capacity shortage and the increasing number of natural catastrophes in recent years, however, the introduction of a viable substitute to reinsurance is viewed by the insurance industry to be both timely and desirable.

Unlike reinsurance negotiations that are costly, lengthy, and irreversible, insurance futures and call spreads - because they are standardized and exchange-traded - have the advantages of reversibility, transactional efficiency, and anonymity.(1) Besides underwriters, mainstream institutional investors may also enjoy the diversification effect of these derivatives since catastrophic losses show no correlation with the price movements of stocks and bonds. However, trading of CAT futures has dwindled to nearly nil according to a report in Institutional Investor (November 1994). Investment managers who are supposed to sell the contracts believe the risk involved is too great.(2) Meanwhile, insurers and risk managers appear to be more interested in buying CAT spreads, resembling layers or excess-of-loss reinsurance agreements, for high-risk coverage. They also like both the cheap price (typically a few thousand dollars per contract) and the much lower risk that the potential payout is limited to a fraction of the loss ratios. At the end of 1993, there was open interest of only 300 contracts, but by December 1994 the figure was over 6,000, with the most popular contract being the "third quarter eastern," which covers the U.S. east coast's hurricane season (July, August, and September).(3)

The success of the CAT call spread contract warrants accurate pricing. However, despite the fact that actuaries have long modeled insurance claim accumulation using a compound Poisson process, the insurance industry employs the standard Black (1976) futures option pricing model (see Chicago Board of Trade, 1995) to price the contract. Black's model is an extension of the well-known Black-Scholes (1973) European option pricing model by assuming the underlying futures price process follows a Brownian motion.(4) The diffusion assumption ignores the sporadic nature of catastrophes and the subsequent concentration of (or jump in) the number of claims, and thus may lead to significant pricing errors. Whaley (1986) tests an American version of the Black model on SP-500 index futures options and finds that, during the 1983 testing period, there was a "moneyness" bias as well as a "maturity" bias. Since Whaley, no significant empirical study has reported on other futures options contracts. Similar pricing errors are found in tests of the Black-Scholes model using spot options and currency options. For example, Rubinstein (1985) finds that the Black-Scholes formula consistently undervalues out-of-the-money short-maturity options, because it ignores the fact that a significant jump may bring an option back into the money.(5) Bodurtha and Courtadon (1987) find that, for currency options with maturities less than 30 days, the degree of underpricing for out-of-the-money options was as high as 28.63 percent, and the overpricing for at-the-money options was as high as 9.61 percent. (However, the overpricing for in-the-money options was only 1.02 percent.)(6)

These results may be explained partly by the fact that the option's underlying asset's risk stems from random jumps, or surprises, rather than diffusion changes, or that the distribution of the underlying asset is leptokurtic. …

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