PRICING CATASTROPHE INSURANCE FUTURES CALL SPREADS - A RANDOMIZED OPERATIONAL TIME APPROACH

Actuaries value insurance claim accumulations using a compound Poisson process to capture the random, discrete, and clustered nature of clai m arrival, but the standard Black (1976) formula for pricing futures o ptions assumes that the underlying futures price follows a pure diffus ion. Extant jump-diffusion option valuation models either assume diver sifiable jump risk or resort to equilibrium arguments to account for j ump risk premiums. We propose a novel randomized operational time appr oach to price options in information-time. The time change transforms a compound Poisson process to a more trackable pure diffusion and lead s to a parsimonious option pricing formula as a risk-neutral Poisson s um of Black's prices in information-time with only two unobservable va riables-the information arrival intensity and the information-time fut ures volatility.