Pricing catastrophe insurance futures call spreads: A randomized operational time approach

Actuaries value insurance claim accumulations using a compound Pois- son process to capture the random, discrete, and clustered nature of claim arrival, but the standard Black (1976) formula for pricing futures options assumes that the underlying futures price follows a pure diffu- sion. Extant jump-diffusion option valuation models either assume di- versifiable jump risk or resort to equilibrium arguments to account for jump risk premiums. We propose a novel randomized operational time approach to price options in information-time. The time change trans- forms a compound Poisson process to a more trackable pure diffusion and leads to a parsimonious option pricing formula as a risk-neutral Poisson sum of Black's prices in information-time with only two unob- servable variables-the information arrival intensity and the informa- tion-time futures volatility.