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Equilibrium Pricing Transforms: New Results Using Buhlmann’s 1980 Economic Model

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  • Wang, Shaun S.

Abstract

In this paper we revisit an economic model of Buhlmann (ASTIN Bulletin, 1980) and derive equilibrium pricing transforms. We obtain the Esscher Transform and the Wang Transform under different sets of assumptions on the aggregate economic environment. We show that the Esscher Transform and the Wang Transform exhibit very different behaviors when used in pricing insurance risks.

Suggested Citation

  • Wang, Shaun S., 2003. "Equilibrium Pricing Transforms: New Results Using Buhlmann’s 1980 Economic Model," ASTIN Bulletin, Cambridge University Press, vol. 33(1), pages 57-73, May.
    • Handle: RePEc:cup:astinb:v:33:y:2003:i:01:p:57-73_01
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    Cited by:

    1. Kijima, Masaaki & Motomiya, Shin-ichi & Suzuki, Yoichi, 2010. "Pricing of CDOs based on the multivariate Wang transform," Journal of Economic Dynamics and Control, Elsevier, vol. 34(11), pages 2245-2258, November.
    2. Boyer, M. Martin & Stentoft, Lars, 2013. "If we can simulate it, we can insure it: An application to longevity risk management," Insurance: Mathematics and Economics, Elsevier, vol. 52(1), pages 35-45.
    3. Johnston, Mark, 2009. "Extending the Basel II approach to estimate capital requirements for equity investments," Journal of Banking & Finance, Elsevier, vol. 33(6), pages 1177-1185, June.
    4. Frédéric Godin & Van Son Lai & Denis-Alexandre Trottier, 2019. "A general class of distortion operators for pricing contingent claims with applications to CAT bonds," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2019(7), pages 558-584, August.
    5. Hung Nguyen & Uyen Pham & Hien Tran, 2012. "On some claims related to Choquet integral risk measures," Annals of Operations Research, Springer, vol. 195(1), pages 5-31, May.
    6. Cairns, Andrew J.G. & Blake, David & Dowd, Kevin, 2006. "Pricing Death: Frameworks for the Valuation and Securitization of Mortality Risk," ASTIN Bulletin, Cambridge University Press, vol. 36(1), pages 79-120, May.
    7. Goovaerts, Marc J. & Laeven, Roger J.A., 2008. "Actuarial risk measures for financial derivative pricing," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 540-547, April.
    8. Chen, Hua & Cox, Samuel H. & Wang, Shaun S., 2010. "Is the Home Equity Conversion Mortgage in the United States sustainable? Evidence from pricing mortgage insurance premiums and non-recourse provisions using the conditional Esscher transform," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 371-384, April.
    9. Masaaki Kijima & Akihisa Tamura, 2014. "Buhlmann’s Economic Premium Principle in The Presence of Transaction Costs," KIER Working Papers 893, Kyoto University, Institute of Economic Research.
    10. Kijima, Masaaki & Muromachi, Yukio, 2008. "An extension of the Wang transform derived from Bühlmann's economic premium principle for insurance risk," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 887-896, June.
    11. Lau, John W. & Siu, Tak Kuen, 2008. "On option pricing under a completely random measure via a generalized Esscher transform," Insurance: Mathematics and Economics, Elsevier, vol. 43(1), pages 99-107, August.
    12. Russo, Vincenzo & Giacometti, Rosella & Ortobelli, Sergio & Rachev, Svetlozar & Fabozzi, Frank J., 2011. "Calibrating affine stochastic mortality models using term assurance premiums," Insurance: Mathematics and Economics, Elsevier, vol. 49(1), pages 53-60, July.
    13. Labuschagne, Coenraad C.A. & Offwood, Theresa M., 2010. "A note on the connection between the Esscher-Girsanov transform and the Wang transform," Insurance: Mathematics and Economics, Elsevier, vol. 47(3), pages 385-390, December.
    14. Energy Sonono, Masimba & Phillip Mashele, Hopolang, 2016. "Estimation of bid-ask prices for options on LIBOR based instruments," Finance Research Letters, Elsevier, vol. 19(C), pages 33-41.

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