A stochastic exposure model for seismic risk assessment and pricing of catastrophe bonds

Abstract

Risk-based catastrophe bonds require the estimation of losses from the convolution of hazard, exposure and vulnerability models. These models are affected by different uncertainties that arise from the definition of their input parameters. In this paper, we propose a stochastic approach to treat the uncertainty in the asset location and attributes of the exposure model. The proposed method uses the Monte Carlo sampling approach to generate a stochastic exposure database, where each asset location is generated randomly within the geometric bound of the administration, while the asset attributes (i.e. construction type and material, number of storey, building activity type and number of dwelling) are sampled from distributions built from census data. Finally, a sensitivity analysis is performed to investigate the influence of the spatial resolution of the exposure model on the average annual losses (AAL) and catastrophe bond prices. To this end, we implement four exposure models, with spatial resolution at the asset, municipality and province levels, on a study region comprising ten provinces in southern Italy. Compared to the proposed model, the exposure model where assets are relocated and aggregated at the geometric centroid of the municipality underestimates AAL by 8%, while a higher difference (up to 20%) is observed for the exposure model where assets are relocated and aggregated at the geometric centroid of the province. We also consider an exposure model whose asset locations are extracted from publicly available building footprints. Yet, this latter model was incomplete for some provinces resulting in underestimation of AAL up to 90%. Differences in catastrophe bond prices obtained from the four exposure models are less evident, with the exposure model built based on the building footprints showing a difference up to 9.5%.