Effect of Uncertainties in Modeling Tropical Cyclones on Pricing of Catastrophe Bonds:A Case Study

Abstract

The insurance industry, in general, accepts large risks due to the combined severity and frequency of catastrophic events; further, these risks are poorly defined given the small amount of data available for extreme events. It is important for the equitable transfer of risk to understand and quantify this risk as accurately as possible. As this risk is propagated to the capital markets, more and more parties will be exposed. An important part of pricing insurance‐linked securities (ILS) is quantifying the uncertainties existing in the physical parameters of the catastrophe models, including both the hazard and damage models. Given the amount of reliable data (1945 till present) on important storm parameters such as central pressure drop, radius to maximum winds, and non‐stationarity of the occurrence rate, moments estimated for these parameters are not highly reliable and knowledge uncertainty must be considered. Also, the engineering damage model for a given class of building in a large portfolio is subject to uncertainty associated with the quality of the buildings. A sample portfolio is used to demonstrate the impact of these knowledge uncertainties. Uncertainties associated with variability of statistics on central pressure drop, occurrence rate, and building quality were estimated and later propagated through a tropical cyclone catastrophe model to quantify the uncertainty of PML results. Finally their effect on the pricing of a typical insurance‐linked security (ILS) was estimated. Statistics of spread over LIBOR given different bond ratings/probability of attachment are presented using a pricing model (Lane [2000]). For a typical ILS, a relatively large coefficient of variation for both probability of attachment and spread over LIBOR was observed. This in turn leads to a rather large price uncertainty for a typical layer and may explain why rational investors expect a higher return for assuming catastrophe risk. The results hold independent of pricing model used. The objective of this study is to quantify this uncertainty for a simple call option and demonstrate its effect on pricing.