Valuing Catastrophe Derivatives Under Limited Diversification: A Stochastic Dominance Approach

Abstract

We present a new approach to the pricing of catastrophe event derivatives that does not assume a fully diversifiable event risk. Instead, we assume that the event occurrence and intensity affect the return of the market portfolio of an agent that trades in the event derivatives. Based on this approach, we derive values for a CAT option and a reinsurance contract on an insurer’s assets using recent results from the option pricing literature. We show that the assumption of unsystematic event risk seriously underprices the CAT option. Last, we present numerical results for our derivatives using real data from hurricane landings in Florida.

Keywords: catastrophe events, jump processes, jump-diffusion, insurance products, derivative assets

JEL Classification: G13