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Pricing Bounds on Asian Options

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  • Nielsen, J. Aase
  • Sandmann, Klaus

Abstract

This paper aims to develop and compare bounds on the pricing formulas for European type discrete Asian options. The lower bound is found by conditioning the maturity payment of the Asian option by the geometric average and the bound derived can be expressed as a portfolio of delayed payment European call options. Several exercise price-dependent upper bounds are derived. Like the lower bound, one of the upper bounds is expressed as a portfolio of delayed payment European call options. Through a numerical analysis, we conclude that more information is gained from the readily calculated bounds than from the usually applied pricing approximations. From the closed-form solutions of the bounds, hedging positions are finally derived.

Suggested Citation

  • Nielsen, J. Aase & Sandmann, Klaus, 2003. "Pricing Bounds on Asian Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 38(2), pages 449-473, June.
    • Handle: RePEc:cup:jfinqa:v:38:y:2003:i:02:p:449-473_00
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    References listed on IDEAS

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    1. Moshe Arye Milevsky & Steven E. Posner, 1999. "Asian Options, The Sum Of Lognormals, And The Reciprocal Gamma Distribution," World Scientific Book Chapters, in: Marco Avellaneda (ed.), Quantitative Analysis In Financial Markets Collected Papers of the New York University Mathematical Finance Seminar, chapter 7, pages 203-218, World Scientific Publishing Co. Pte. Ltd..
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    5. Klaus Sandmann & J. Aase Nielsen, 2002. "Pricing of Asian exchange rate options under stochastic interest rates as a sum of options," Finance and Stochastics, Springer, vol. 6(3), pages 355-370.
    6. Turnbull, Stuart M. & Wakeman, Lee Macdonald, 1991. "A Quick Algorithm for Pricing European Average Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 26(3), pages 377-389, September.
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