Pricing industry loss warranties in a Lévy–Frailty framework

Abstract

We propose a novel risk-neutral pricing approach for industry loss warranties. In doing so, we explicitly take into account the statistical dependence of the losses on individual policies in the underlying insurance portfolio, caused by the occurrence of a natural catastrophe. Inspired by recent advances in the structured credit literature, we model joint claim events in a Lévy–Frailty framework with a stochastic time change. Event time is driven by rare and large jumps of a compound Poisson subordinator and thus elapses more quickly when a natural catastrophe has struck, leading to a clustering of losses. We estimate the model on historical ILW quotes and obtain encouraging fit statistics.