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Contingent claim pricing using probability distortion operators: methods from insurance risk pricing and their relationship to financial theory


  • Mahmoud Hamada
  • Michael Sherris


This paper considers the pricing of contingent claims using an approach developed and used in insurance pricing. The approach is of interest and significance because of the increased integration of insurance and financial markets and also because insurance-related risks are trading in financial markets as a result of securitization and new contracts on futures exchanges. This approach uses probability distortion functions as the dual of the utility functions used in financial theory. The pricing formula is the same as the Black-Scholes formula for contingent claims when the underlying asset price is log-normal. The paper compares the probability distortion function approach with that based on financial theory. The theory underlying the approaches is set out and limitations on the use of the insurance-based approach are illustrated. The probability distortion approach is extended to the pricing of contingent claims for more general assumptions than those used for Black-Scholes option pricing.

Suggested Citation

  • Mahmoud Hamada & Michael Sherris, 2003. "Contingent claim pricing using probability distortion operators: methods from insurance risk pricing and their relationship to financial theory," Applied Mathematical Finance, Taylor & Francis Journals, vol. 10(1), pages 19-47.
  • Handle: RePEc:taf:apmtfi:v:10:y:2003:i:1:p:19-47 DOI: 10.1080/1350486032000069580

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    Cited by:

    1. Hammoudeh, Shawkat & McAleer, Michael, 2013. "Risk management and financial derivatives: An overview," The North American Journal of Economics and Finance, Elsevier, vol. 25(C), pages 109-115.
    2. Massimiliano Corradini & Andrea Gheno, 2007. "Contingent Claim Pricing In A Dual Expected Utility Theory Framework," Departmental Working Papers of Economics - University 'Roma Tre' 0082, Department of Economics - University Roma Tre.
    3. Mahmoud Hamada & Emiliano A. Valdez, 2008. "CAPM and Option Pricing With Elliptically Contoured Distributions," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 75(2), pages 387-409.
    4. Dominique Guegan & Bertrand Hassani & Kehan Li, 2017. "An alternative class of distortion operators alternative tools to generate asymmetrical multimodal distributions," Documents de travail du Centre d'Economie de la Sorbonne 17030, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    5. Dominique Guegan & Bertrand Hassani & Kehan Li, 2017. "An alternative class of distortion operators," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01543251, HAL.
    6. Corradini, M. & Gheno, A., 2009. "Incomplete financial markets and contingent claim pricing in a dual expected utility theory framework," Insurance: Mathematics and Economics, Elsevier, vol. 45(2), pages 180-187, October.
    7. Choe, Geon Ho & Koo, Ki Hwan, 2014. "Probability of multiple crossings and pricing of double barrier options," The North American Journal of Economics and Finance, Elsevier, vol. 29(C), pages 156-184.
    8. Labuschagne, Coenraad C.A. & Offwood, Theresa M., 2013. "Pricing exotic options using the Wang transform," The North American Journal of Economics and Finance, Elsevier, vol. 25(C), pages 139-150.
    9. Denuit Michel & Dhaene Jan & Goovaerts Marc & Kaas Rob & Laeven Roger, 2006. "Risk measurement with equivalent utility principles," Statistics & Risk Modeling, De Gruyter, vol. 24(1/2006), pages 1-25, July.
    10. Alexis Bienvenüe & Didier Rullière, 2012. "Iterative Adjustment of Survival Functions by Composed Probability Distortions," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 37(2), pages 156-179, September.
    11. Balbás, Alejandro & Balbás, Beatriz & Balbás, Raquel, 2010. "CAPM and APT-like models with risk measures," Journal of Banking & Finance, Elsevier, vol. 34(6), pages 1166-1174, June.


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