The Economics of Extreme events: Pricing Mechanisms and Quantitative Modeling in the CAT Bond Market

Catastrophic bonds (CAT bonds) represent one of the most significant innovations and rapidly expanding segments of the insurance-linked securities market, enabling the transfer of low-frequency and high-severity natural catastrophe risks from insurers and reinsurers to global capital market investors. Unlike conventional fixed-income securities, CAT bonds are exposed to perils that are exogenous to financial markets-such as earthquakes, hurricanes, storms-whose statistical properties significantly diverge from the classical assumptions of market efficiency, arbitrage-free pricing and hedgeability. The presence of extreme tail distributions, structural event clustering, climate-driven non-stationarity and geographical concentration of exposures makes catastrophe risk a paradigmatic example of non-tradable, incomplete -market risk. As a consequence, CAT bond pricing cannot be derived from purely arbitrage-based frameworks and requires a synthesis of financial, actuarial and behavioral principles to accurately reflect both expected losses and investors risk preferences. This thesis provides a comprehensive and multidisciplinary analysis of the pricing of CAT bonds, integrating insights from equilibrium finance, actuarial science, utility theory, probability distortions and reduced-form hazard-intensity models. The study is structured to bridge theoretical modeling with empirical relevance, and culminates in the construction of a Monte Carlo simulation framework capable of replicating realistic catastrophe loss dynamics and evaluating their impact on CAT bond spreads across different trigger structures and modeling assumptions. the first part of the thesis develops the arbitrage-based and reduced-form modeling foundations, including Poisson, mixed-Poisson, Cox processes and compound loss distributions, which capture the stochastic structure of catastrophe frequency and severity. The study then examines key equilibrium formulations-most highlighting how jump risks and consumption shocks generate systematic risk premia. Preference-based approaches, such as those of Embrechts and Mister (1997), Case (1999), and Young (2004), are analyzed to show how investor utility, certainty equivalents, and risk absorption capacity influence CAT bond spreads, especially in incomplete markets. Furthermore, the thesis explores the role of probability distortions and the Wang transform in deriving risk-adjusted exceedance curves, as well as industry pricing metrics-including Expected Loss (EL), Conditional Expected Loss (CEL), Probability of First Loss (PFL), and expected-loss multiples-used in market practice. The empirical component applies these modeling frameworks to a Monte Carlo simulation of catastrophic loss processes, generating synthetic loss distributions and evaluating their impact on CAT bond spreads and expected-loss multiple. The simulation incorporates heavy-tailed severity distributions, time-varying hazard rates, and alternative trigger mechanism, allowing for a realistic assessment of pricing sensitivities. The findings illustrate how catastrophe intensity, trigger design, and risk-loading assumptions significantly affect model-implied spreads, and how preference-based valuations diverge from purely actuarial pricing principles. Overall, the thesis demonstrates that no single pricing paradigm fully captures the complexity of CAT bond markets. Instead, a multifaceted approach - combining actuarial, financial, and behavioral elements-is required to realistically characterize risk premia and inform both academic research and market practice.