A Unified Bayesian Framework for Pricing Catastrophe Bond Derivatives

TL;DR

This paper introduces a comprehensive Bayesian framework for pricing catastrophe bonds that incorporates uncertainty in catastrophe events and interest rates, providing a more flexible and reliable approach to understanding risk premia.

Contribution

It presents a unified Bayesian asset pricing model for CAT bonds, integrating complex catastrophe risk beliefs and stochastic interest rates within a novel hierarchical risk model.

Findings

Clusters reveal relationships between CAT bond prices and claim characteristics

Model captures diverse catastrophe risk profiles effectively

Framework enables empirical analysis of risk premia

Abstract

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.