Abstract

An Application of Piecewise Deterministic Processes to the Pricing of Catastrophe Options

Alexander Muermann

London School of Economics

In recent years there has been an ongoing economic and political debate of whether financial markets should be used to insure risk that has been traditionally hedged through other channels. Famous examples include the discussion about the change to a funded pension scheme, equity-linked life insurance contracts, and catastrophe options. This need for an alternative way of insurance to traditional insurance resulted in a growing number of insurance products coming onto the market and containing a financial component of some sort. The demand of the insurance industry for financial capital suggests to combine the methodologies used in both areas, insurance mathematics and mathematical finance. In the present paper we are focusing on insurance derivatives being introduced at the Chicago Board of Trade (CBOT) in 1992. We model the underlying index which is measuring the losses due to catastrophes as a piecewise deterministic process. The theory of this class of stochastic processes enables us to derive an integro-differential equation for the price of such insurance derivatives.