A general class of distortion operators for pricing contingent claims with applications to CAT bonds. (English) Zbl 1422.91695
Summary: The current paper provides a general approach to construct distortion operators that can price financial and insurance risks. Our approach generalizes the
[S. S. Wang, “A class of distortion operators for pricing financial and insurance risks”, J. Risk Insur. 67, No. 1, 15–36 (2000; doi:10.2307/253675)] 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.
MSC:
| 91G20 | Derivative securities (option pricing, hedging, etc.) |
| 91B30 | Risk theory, insurance (MSC2010) |
| 62P05 | Applications of statistics to actuarial sciences and financial mathematics |
Keywords:
distortion operator; Wang transform; distortion risk measure; arbitrage-free pricing; insurance pricing; contingent claim pricing; CAT bondsReferences:
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