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Pricing exotic options using the Wang transform

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  • Labuschagne, Coenraad C.A.
  • Offwood, Theresa M.

Abstract

The Wang transform allows for a simple, yet intuitive approach to pricing options with underlying based on geometric Brownian motion. This paper shows how the approach by Hamada and Sherris can be used to price some exotic options. Examples showing the convergence of the Wang price to the Black–Scholes price for a Margrabe option, a geometric basket option and an asset-or-nothing option are given. We also take a look at the range of prices achievable using the Wang transform for these options.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ecofin:v:25:y:2013:i:c:p:139-150
    DOI: 10.1016/j.najef.2012.06.008
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    References listed on IDEAS

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    1. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    2. Kijima, Masaaki, 2006. "A Multivariate Extension of Equilibrium Pricing Transforms: The Multivariate Esscher and Wang Transforms for Pricing Financial and Insurance Risks," ASTIN Bulletin, Cambridge University Press, vol. 36(1), pages 269-283, May.
    3. A. Chateauneuf & R. Kast & A. Lapied, 1996. "Choquet Pricing For Financial Markets With Frictions1," Mathematical Finance, Wiley Blackwell, vol. 6(3), pages 323-330, July.
    4. Wang, Shaun S., 2002. "A Universal Framework for Pricing Financial and Insurance Risks," ASTIN Bulletin, Cambridge University Press, vol. 32(2), pages 213-234, November.
    5. 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.
    6. 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.
    7. Pelsser, Antoon, 2008. "On the Applicability of the Wang Transform for Pricing Financial Risks," ASTIN Bulletin, Cambridge University Press, vol. 38(1), pages 171-181, May.
    8. Margrabe, William, 1978. "The Value of an Option to Exchange One Asset for Another," Journal of Finance, American Finance Association, vol. 33(1), pages 177-186, March.
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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. 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.
    3. Frédéric Godin & Van Son Lai & Denis-Alexandre Trottier, 2019. "A General Class of Distortion Operators for Pricing Contingent Claims with Applications to CAT Bonds," Working Papers 2019-004, Department of Research, Ipag Business School.

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    More about this item

    Keywords

    Wang transform; Exotic options; Geometric Brownian motion; Choquet pricing;
    All these keywords.

    JEL classification:

    • C20 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - General
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
    • G24 - Financial Economics - - Financial Institutions and Services - - - Investment Banking; Venture Capital; Brokerage

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