Catastrophe risk bonds with applications to earthquakes

Catastrophe (CAT) risk bonds provide a solid mechanism for direct transfer of the financial consequences of extreme events (hazards) into the financial market. During the past two decades, insurance companies have been searching for more adequate liquidity funds as a consequence of increasing losses due to climate change and severe natural disasters. The aims of this study were twofold. First, we study the pricing process for CAT bonds for the structure of \(n\) financial and \(m\) catastrophe-independent risks. Second, to illustrate the applicability of our results, an application for earthquakes is considered using extreme value theory. As a numerical example, a CAT bond with historical data from California is proposed in which the magnitude, latitude, longitude, and depth are included in the model. In addition, appropriate models are constructed for the term structure of interest and inflation rate dynamics, and a stochastic process for the coupon rate. Finally, on the basis of analysis for the aforementioned catastrophe and financial market risks, we can use equilibrium pricing theory to find a certain value price for the CAT California earthquake bond.