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On the Hedging Portfolio of Asian Options

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  • Jacques, Michel

Abstract

We give 2 explicit formulae for the hedging portfolio of Asian options. One is based on the usual Lognormal approximation, and the other on an Inverse Gaussian approximation. Both give excellent results as replicating strategies when the parameters of the model are in a reasonable range.

Suggested Citation

  • Jacques, Michel, 1996. "On the Hedging Portfolio of Asian Options," ASTIN Bulletin, Cambridge University Press, vol. 26(2), pages 165-183, November.
    • Handle: RePEc:cup:astinb:v:26:y:1996:i:02:p:165-183_00
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    Cited by:

    1. Simon, S. & Goovaerts, M. J. & Dhaene, J., 2000. "An easy computable upper bound for the price of an arithmetic Asian option," Insurance: Mathematics and Economics, Elsevier, vol. 26(2-3), pages 175-183, May.
    2. Manuel Moreno & Javier F. Navas, 2003. "Australian Asian Options," Working Papers 28, Barcelona School of Economics.
    3. Benhamou, Eric & Duguet, Alexandre, 2003. "Small dimension PDE for discrete Asian options," Journal of Economic Dynamics and Control, Elsevier, vol. 27(11), pages 2095-2114.
    4. Zhaojun Yang & Christian-Oliver Ewald & Olaf Menkens, 2011. "Pricing and hedging of Asian options: quasi-explicit solutions via Malliavin calculus," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 74(1), pages 93-120, August.
    5. E. Benhamou, 2001. "Fast Fourier Transform for discrete Asian Options," Computing in Economics and Finance 2001 6, Society for Computational Economics.
    6. Alain Chateauneuf & Mina Mostoufi & David Vyncke, 2015. "Comonotonic Monte Carlo and its applications in option pricing and quantification of risk," Documents de travail du Centre d'Economie de la Sorbonne 15015, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    7. Serguei Pergamenchtchikov & Alena Shishkova, 2020. "Hedging problems for Asian options with transactions costs," Papers 2001.01443, arXiv.org.
    8. Jr-Yan Wang & Hsiao-Chuan Wang & Yi-Chen Ko & Mao-Wei Hung, 2017. "Rainbow trend options: valuation and applications," Review of Derivatives Research, Springer, vol. 20(2), pages 91-133, July.
    9. Dhaene, J. & Denuit, M. & Goovaerts, M. J. & Kaas, R. & Vyncke, D., 2002. "The concept of comonotonicity in actuarial science and finance: applications," Insurance: Mathematics and Economics, Elsevier, vol. 31(2), pages 133-161, October.
    10. Ewald, Christian-Oliver & Menkens, Olaf & Hung Marten Ting, Sai, 2013. "Asian and Australian options: A common perspective," Journal of Economic Dynamics and Control, Elsevier, vol. 37(5), pages 1001-1018.
    11. Eric Benhamou & Alexandre Duguet, 2000. "A 2 Dimensional Pde For Discrete Asian Options," Computing in Economics and Finance 2000 33, Society for Computational Economics.
    12. Schepper, Ann De & Heijnen, Bart, 2007. "Distribution-free option pricing," Insurance: Mathematics and Economics, Elsevier, vol. 40(2), pages 179-199, March.
    13. Aprahamian, Hrayer & Maddah, Bacel, 2015. "Pricing Asian options via compound gamma and orthogonal polynomials," Applied Mathematics and Computation, Elsevier, vol. 264(C), pages 21-43.
    14. Geon Ho Choe & Minseok Kim, 2021. "Closed‐form lower bounds for the price of arithmetic average Asian options by multiple conditioning," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 41(12), pages 1916-1932, December.
    15. Jacques, Michel, 1997. "The Istanbul option: Where the standard European option becomes Asian," Insurance: Mathematics and Economics, Elsevier, vol. 21(2), pages 139-152, November.

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