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

Ning Ma ()
Additional contact information
Ning Ma: School of Statistics, Renmin University of China, Beijing 100872, China

Mathematics, 2025, vol. 13, issue 19, 1-26

Abstract: 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.

Keywords: CAT bond; aggregate loss; distortion operator; Esscher transform; Wang transform (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/19/3113/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/19/3113/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:13:y:2025:i:19:p:3113-:d:1760744

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().