Average Rate Claims with Emphasis on Catastrophe Loss Options

This article studies the valuation of options written on the average level of a Markov process. The general properties of such options are examined. We propose a closed-form characterization in which the option payoff is contingent on cumulative catastrophe losses. In our framework, the loss rate is a mean-reverting Markov process, with no continuous martingale component. The model supposes that high loss levels have lower arrival rates. We analytically derive the cumulative loss process and its characteristic function. The resulting option model is promising.