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Catastrophe (CAT) bond markets are incomplete and hence carry uncertainty ininstrument pricing. As such various pricing approaches have been proposed, butnone treat the uncertainty in catastrophe occurrences and interest rates in asufficiently flexible and statistically reliable way within a unifying assetpricing framework. Consequently, little is known empirically about the expectedrisk-premia of CAT bonds. The primary contribution of this paper is to presenta unified Bayesian CAT bond pricing framework based on uncertaintyquantification of catastrophes and interest rates. Our framework allows forcomplex beliefs about catastrophe risks to capture the distinct and commonpatterns in catastrophe occurrences, and when combined with stochastic interestrates, yields a unified asset pricing approach with informative expected riskpremia. Specifically, using a modified collective risk model -- DirichletPrior-Hierarchical Bayesian Collective Risk Model (DP-HBCRM) framework -- wemodel catastrophe risk via a model-based clustering approach. Interest raterisk is modeled as a CIR process under the Bayesian approach. As a consequenceof casting CAT pricing models into our framework, we evaluate the price andexpected risk premia of various CAT bond contracts corresponding to clusteringof catastrophe risk profiles. Numerical experiments show how these clustersreveal how CAT bond prices and expected risk premia relate to claim frequencyand loss severity.

A Unified Bayesian Framework for Pricing Catastrophe Bond Derivatives