On Modelling and Pricing Index Linked Catastrophe Derivatives

Abstract

We consider the problem of indifference pricing of derivatives written on CAT bonds. The industrial loss index is modeled by a compound Poisson process and the number of claims as doubly stochastic process, such that its intensity varies over time. The insurer can adjust her portfolio by choos- ing the risk loading, which in turn determines the demand. We probably restrict the policies of the insurance company in a way that does not permit changing the risk loading during catastrophe times. We compute the price of a CAT option written on that index using utility indifference pricing