A General Class of Distortion Operators for Pricing Contingent Claims with Applications to CAT Bonds
Forthcoming Scandinavian Actuarial Journal
48 Pages Posted: 21 Aug 2017 Last revised: 12 Feb 2019
Date Written: February 10, 2019
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.
Keywords: Distortion operator, Arbitrage-free pricing, Wang transform, Insurance pricing, Contingent claim pricing, Pricing of CAT bonds, Distortion risk measure
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