A CAT Bond Pricing Model Based on the Distortion of Aggregate Loss Distributions

Pricing catastrophe (CAT) bonds in incomplete markets poses persistent challenges, particularly in converting risk from the real-world measure to the pricing measure. The commonly used Wang transform focuses on distorting the loss severity distribution, which may underestimate catastrophe risk. This paper proposes a new distortion operator based on the Esscher transform that distorts the aggregate loss distribution rather than focusing solely on the severity or frequency components. The proposed approach provides more comprehensive risk adjustment, making it well-suited for the distributional characteristics of catastrophic loss indicators. Its applicability is demonstrated via an application to Chinese earthquake data. Monte Carlo simulation was used to compare pricing results via the distortion of different components. By reformulating the proposed distortion method into the form of a distortion operator and comparing it with the Wang transform, this paper demonstrates that the proposed approach offers significantly enhanced analytical tractability for complex distributions. It enables a more transparent analysis of the transformed distribution and its implications for bond pricing mechanisms.