Stable Weak Approximation at Work in Index-Linked Catastrophe Bond Pricing

We consider the subject of approximating tail probabilities in the general compound renewal process framework, where severity data are assumed to follow a heavy-tailed law (in that only the first moment is assumed to exist). By using weak convergence of compound renewal processes to Lévy motion, we derive such weak approximations. Their applicability is then highlighted in the context of an existing, classical, index-linked catastrophe bond pricing model, and in doing so we specialise these approximations to the case of a compound time-inhomogeneous Poisson process. We emphasise a unique feature of our approximation, in that it only demands finiteness of the first moment of the aggregate loss processes. Finally, a numerical illustration is presented. The behaviour of our approximations is compared to both Monte Carlo simulations and first-order single risk loss process approximations, and compares favourably