A general class of distortion operators for pricing contingent claims with applications to CAT bonds. Issue 7 (9th August 2019)

• Record Type: Journal Article
• Authors: Godin, Frédéric; Lai, Van Son; Trottier, Denis-Alexandre
• Is Part Of: Scandinavian actuarial journal. Volume 2019:Issue 7(2019)
• Page Start: 558
• Page End: 584
• Publication Date: 2019-08-09
• Subjects: Distortion operator -- Wang transform -- distortion risk measure -- arbitrage-free pricing -- insurance pricing -- contingent claim pricing -- CAT bonds; Insurance, Life -- Mathematics -- Periodicals; Insurance -- Mathematics -- Periodicals; 368.01
• DOI: 10.1080/03461238.2019.1581837
• Languages: English
• ISSNs: 0346-1238

Abstract

ABSTRACT: The current paper provides a general approach to construct distortion operators that can price financial and insurance risks. Our approach generalizes the (Wang 2000) transform and recovers multiple distortions proposed in the literature as particular cases. This approach enables designing distortions that are consistent with various pricing principles used in finance and insurance such as no-arbitrage models, equilibrium models and actuarial premium calculation principles. Such distortions allow for the incorporation of risk-aversion, distribution features (e.g. skewness and kurtosis) and other considerations that are relevant to price contingent claims. The pricing performance of multiple distortions obtained through our approach is assessed on CAT bonds data. The current paper is the first to provide evidence that jump-diffusion models are appropriate for CAT bonds pricing, and that natural disaster aversion impacts empirical prices. A simpler distortion based on a distribution mixture is finally proposed for CAT bonds pricing to facilitate the implementation.