Natural catastrophe risk is increasingly covered through alternative capital instead of classical reinsurance. As most instruments in this space do not trade in a secondary market, their ongoing valuation poses a challenge to investors. We suggest extracting pricing information contained in regularly observed catastrophe bond quotes by means of a reduced form model. The resulting implied Poisson intensities are shown to materially depend on the time to maturity and modeled probability of first loss. Along these two dimensions, we estimate smooth hazard rate surfaces that allow investors to mark illiquid catastrophe risk contracts to market.
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.
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