We model claim arrival and loss uncertainties jointly in a doubly-binomial framework to price an Asian-style catastrophe (CAT) option with a non-traded underlying loss index using the no-arbitrage martingale pricing methodology. We span these uncertainties by benchmarking to the shadow price of...

Actuaries value insurance claim accumulations using a compound Poisson 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 diffusion. Extant...