A QUADRATIC HEDGING APPROACH TO COMPARISON OF CATASTROPHE INDICES

The present study addresses the problem of designing a catastrophe derivative that insurers can use to hedge catastrophe-related losses in an incomplete market. The losses are modeled as a doubly stochastic compound Poisson process with shot-noise intensity. The hedging capability of a derivative is measured by the reduction of the mean squared hedging error resulting from optimal trading in the derivative. A general form of this measure is obtained in terms of the coefficients in the martingale dynamics of the loss process and the price process of the derivative. Six specific derivatives, with pay-offs depending in different ways on available catastrophe indices and portfolio data, are compared by the proposed criterion.