Modelling clustering of natural hazard phenomena and the effect on re/insurance loss perspectives

In this paper, we present a conceptual framework for modelling clustered natural hazards that makes use of historical event data as a starting point. We review a methodology for modelling clustered natural hazard processes called Poisson mixtures. This methodology is suited to the application we have in mind as it naturally models processes that yield cross-event correlation (unlike homogeneous Poisson models), has a high degree of tunability to the problem at hand and is analytically tractable. Using European windstorm data as an example, we provide evidence that the historical data show strong evidence of clustering. We then develop Poisson and Clustered simulation models for the data, demonstrating clearly the superiority of the Clustered model which we have implemented using the Poisson mixture approach. We then discuss the implications of including clustering in models of prices of catXL contracts, one of the most commonly used mechanisms for transferring risk between primary insurers and reinsurers. This paper provides a number of unique insights into the impact clustering has on modelled catXL contract prices. The simple modelling example in this paper provides a clear and insightful starting point for practitioners tackling more complex natural hazard risk problems.