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Sharp Upper and Lower Bounds for Basket Options

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  • Peter Laurence
  • Tai-Ho Wang
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    Abstract

    Given a basket option on two or more assets in a one-period static hedging setting, the paper considers the problem of maximizing and minimizing the basket option price subject to the constraints of known option prices on the component stocks and consistency with forward prices and treat it as an optimization problem. Sharp upper bounds are derived for the general n-asset case and sharp lower bounds for the two-asset case, both in closed forms, of the price of the basket option. In the case n�=�2 examples are given of discrete distributions attaining the bounds. Hedge ratios are also derived for optimal sub and super replicating portfolios consisting of the options on the individual underlying stocks and the stocks themselves.

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    Bibliographic Info

    Article provided by Taylor & Francis Journals in its journal Applied Mathematical Finance.

    Volume (Year): 12 (2005)
    Issue (Month): 3 ()
    Pages: 253-282

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    Handle: RePEc:taf:apmtfi:v:12:y:2005:i:3:p:253-282

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    Web page: http://www.tandfonline.com/RAMF20

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    Related research

    Keywords: Basket option; duality; sharp bound;

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    Cited by:
    1. Mathias Beiglböck & Pierre Henry-Labordère & Friedrich Penkner, 2013. "Model-independent bounds for option prices—a mass transport approach," Finance and Stochastics, Springer, vol. 17(3), pages 477-501, July.
    2. Laurence, Peter & Wang, Tai-Ho, 2009. "Sharp distribution free lower bounds for spread options and the corresponding optimal subreplicating portfolios," Insurance: Mathematics and Economics, Elsevier, vol. 44(1), pages 35-47, February.
    3. Pierre Henry-Labordere & Nizar Touzi, 2013. "An Explicit Martingale Version of Brenier's Theorem," Working Papers hal-00790001, HAL.
    4. Arash Fahim & Yu-Jui Huang, 2014. "Model-independent Superhedging under Portfolio Constraints," Papers 1402.2599, arXiv.org.
    5. Pierre Henry-Labordere & Nizar Touzi, 2013. "An Explicit Martingale Version of Brenier's Theorem," Papers 1302.4854, arXiv.org, revised Apr 2013.
    6. Peña, Javier & Vera, Juan C. & Zuluaga, Luis F., 2012. "Computing arbitrage upper bounds on basket options in the presence of bid–ask spreads," European Journal of Operational Research, Elsevier, vol. 222(2), pages 369-376.
    7. D. J. Manuge & P. T. Kim, 2014. "A fast Fourier transform method for Mellin-type option pricing," Papers 1403.3756, arXiv.org, revised Mar 2014.

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