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

See all articles by Frédéric Godin

Frédéric Godin

Concordia University, Quebec - Department of Mathematics & Statistics; Université Laval

Van Son Lai

Université Laval

Denis-Alexandre Trottier

Laval University, Faculté d'Administration, Département de Finance et Assurance, Students

Date Written: February 10, 2019

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.

Keywords: Distortion operator, Arbitrage-free pricing, Wang transform, Insurance pricing, Contingent claim pricing, Pricing of CAT bonds, Distortion risk measure

Suggested Citation

Godin, Frédéric and Lai, Van Son and Trottier, Denis-Alexandre, A General Class of Distortion Operators for Pricing Contingent Claims with Applications to CAT Bonds (February 10, 2019). Forthcoming Scandinavian Actuarial Journal. Available at SSRN: https://ssrn.com/abstract=3020384 or http://dx.doi.org/10.2139/ssrn.3020384

Frédéric Godin (Contact Author)

Concordia University, Quebec - Department of Mathematics & Statistics ( email )

1455 De Maisonneuve Blvd. W.
Montreal, Quebec H3G 1M8
Canada

Université Laval ( email )

2214 Pavillon J-A. DeSeve
Quebec, Quebec G1K 7P4
Canada

Van Son Lai

Université Laval ( email )

FSA ULaval
Quebec G1V 0A6
Canada
418-656-2131, x3943 (Phone)

Denis-Alexandre Trottier

Laval University, Faculté d'Administration, Département de Finance et Assurance, Students ( email )

Pavillon Palasis-Prince
Quebec, Quebec G1K 7P4
Canada

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