Catastrophe bond pricing with extreme value index as a parametric trigger

The escalating frequency of weather-related catastrophes poses significant challenges to the risk management capabilities of (re)insurers. Catastrophe (CAT) bonds serve as a robust mechanism for diversifying these extreme risks and enhancing the resilience of investors’ portfolios. However, the selection of an appropriate trigger mechanism for CAT bonds necessitates a careful balance between moral hazard and basis risk. This study proposes the adoption of the Extreme Value Index (EVI) as a parametric trigger, which effectively captures the intensity of catastrophic risks. By correlating extreme tornado losses with observable covariates to enhance the transparency of CAT bonds, we investigate the spatial heterogeneity of covariates in EVI prediction using the Generalized Geographically Weighted Regression (GGWR) model. A novel GW-XGBoost method is developed by integrating spatially varying coefficients to generate spatially enhanced covariates, thereby achieving accurate EVI prediction and mitigating basis risk. For CAT bond pricing, the conventional Wang transform, based on the Gaussian distribution, tends to underestimate catastrophic risks. Considering the heavy-tailed characteristics of the EVI trigger, we employ an Esscher transform based on the Normal Inverse Gaussian (NIG) distribution as a distortion operator, thereby improving the rationality and accuracy of catastrophe bond valuation. Utilizing Texas tornado data, we design various bond payoff structures and demonstrate the applicability and flexibility of our EVI-based CAT bond pricing model. A sensitivity analysis is conducted to explore the impact of risk spreads and maturity periods on bond prices. The proposed methodology provides a practical approach to enhancing bond transparency and market appeal.