  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.
