Catastrophe (CAT) bonds have become increasingly vital in managing and transferring catastrophic risk. These bonds offer a source of capital to cover losses arising from natural disasters, allowing investors to diversify their portfolios while helping issuers mitigate potentially devastating financial consequences. Understanding the pricing dynamics of CAT bonds is essential, both for investors seeking informed decisions and for issuers optimizing their risk management strategies. This paper introduces a probabilistic machine-learning-based predictive framework for the pricing of CAT bonds, aiming to enhance empirical pricing accuracy and discover previously undetected nonlinear dependence between the key risk factors and CAT bond spreads. Early research by Lane (2000) laid the groundwork for CAT bond pricing literature, proposing a log-linear regression model employing conditional expected loss and probability of first loss as predictors. Subsequent studies expanded on this linear framework, incorporating additional predictors and examining pricing under diverse conditions. Gürtler et al. (2016) incorporated bond characteristics like trigger type and bond rating, while Braun (2016) integrated market condition indices, such as the Lane Synthetic Rate on Line index and the BB corporate bond spread. Götze and Gürtler (2020a) explored sponsor-related pricing inefficiencies across different market conditions, and Morana and Sbrana (2019) focused on the impact of climate change on CAT bond returns. Further extending the research scope, Zhao and Yu (2020) utilized actual catastrophe data to forecast CAT bond prices using market-based methods, Braun et al. (2022) developed factor pricing models for cross-sectional CAT bond returns, and Herrmann and Hibbeln (2023) investigated liquidity premiums in the secondary market.

Catastrophe (CAT) bond markets are incomplete and hence carry uncertainty in instrument pricing. As such various pricing approaches have been proposed, but none treat the uncertainty in catastrophe occurrences and interest rates in a sufficiently flexible and statistically reliable way within a unifying asset pricing framework. Consequently, little is known empirically about the expected risk-premia of CAT bonds. The primary contribution of this paper is to present a unified Bayesian CAT bond pricing framework based on uncertainty quantification of catastrophes and interest rates. Our framework allows for complex beliefs about catastrophe risks to capture the distinct and common patterns in catastrophe occurrences, and when combined with stochastic interest rates, yields a unified asset pricing approach with informative expected risk premia. Specifically, using a modified collective risk model -- Dirichlet Prior-Hierarchical Bayesian Collective Risk Model (DP-HBCRM) framework -- we model catastrophe risk via a model-based clustering approach. Interest rate risk is modeled as a CIR process under the Bayesian approach. As a consequence of casting CAT pricing models into our framework, we evaluate the price and expected risk premia of various CAT bond contracts corresponding to clustering of catastrophe risk profiles. Numerical experiments show how these clusters reveal how CAT bond prices and expected risk premia relate to claim frequency and loss severity.