Valuing Clustering in Catastrophe Derivatives

The role that clustering in activity and/or severity plays in catastrophe modeling and derivative valuation is a key aspect that has been overlooked in the recent literature. Here, we propose two marked point processes to account for these features. The first approach assumes the points are driven by a stochastic hazard rate modulated by a Markov chain while marks are drawn from a regime specific distribution. In the second approach, the points are driven by a self-exciting process while marks are drawn from a fixed distribution. Within this context, we provide a unified approach to efficiently value catastrophe options -- such as those embedded in catastrophe bonds. Our approach is based on deriving the valuation PIDE and utilizes transforms to provide semi-analytical closed form solutions. This contrasts with most prior works where the valuation formulae require computing several infinite sums together with numerical integration