Design and pricing of a transparent parametric-modeled loss CAT bond: application to German windstorm

Abstract

Catastrophe (cat) bonds overcome some lack of reinsurance by sourcing capacity from the wider capital markets. We present a new type of cat bond addressing the known trade-off between moral hazard and basis risk. As our main contributions we propose a trigger mechanism which is entirely transparent and simpler to evaluate compared to indemnity modeling techniques, as well as a methodology to price this cat bond. This is relevant for insurers and public authorities in a world where natural disasters are occurring with increasing frequency and severity due to climate change, but also for players willing to enter the cat bond market for whom the lack of transparency of this asset class has been a significant obstacle. Our trigger is derived from a cost random field which separates the physical hazard, a vulnerability function and the exposure. This allows the trigger to take a flexible form between parametric and modeled loss, in case exposure is taken into account. We present a case study based on historical windstorm events impacting Germany. Using wind speed data from historical storms, we fit a max-stable random field on a resolution which is standard in the reinsurance industry. The availability of industry loss and exposure data allows us to calibrate the vulnerability component to historical observations. Besides measuring the basis risk associated with our trigger, we perform a full model assessment and discuss numerical results.