The Hybrid Frontier: Optimal Trigger Design for Cyber Catastrophe Bonds

Abstract

This thesis investigates whether hybrid parametric-indemnity triggers can be optimally designed for cyber catastrophe (CAT) bonds to reduce basis risk while improving payout efficiency and value. While traditional CAT bonds rely on either indemnity triggers (which provide close-to-precise loss matching but slow payouts) or parametric triggers (which enable rapid liquidity but can in some cases introduce basis risk), the applicability of hybrid triggers (the weighting of both indemnity and parametric structures) to cyber risk remains underexplored. This research extends existing modeling frameworks to cyber-driven disruptions in digital infrastructure. A quantitative model, using Hawkes processes for clustered arrival times, is developed to simulate cyber loss processes and evaluate bond payoff performance under varying trigger compositions. The framework incorporates stochastic event arrivals, loss severity distributions, and discounting effects associated with payout delays. A risk-adjusted net present value (RANPV) metric is used to assess the trade-off between expected returns and variance across different hybrid configurations. The results demonstrate that, among existing public cyber CAT bonds, neither pure indemnity nor pure parametric structures are optimal. Instead, an interior optimum emerges in which a hybrid trigger balances liquidity provision and payout precision. The optimal structure minimizes the trade-off between liquidity and basis risk, forming a concave efficient frontier of cyber CAT bond design. The study also shows that the results are economically viable, not just for the insured party, but also for investors who are insuring digital infrastructure. These findings provide evidence that hybrid trigger structures are not only feasible but are economically optimal for cyber ILS markets. This study contributes to the CAT bond literature by introducing a novel modeling approach using Hawkes processes, tailored to cyber risk, as compared to Poisson processes, offering practical insights for structuring cyber CAT bonds going forward.