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Analytical Valuation of American-Style Asian Options

  • Asbjørn T. Hansen

    ()

    (Global Equities, Dresdner Kleinwort Benson, 20 Fenchurch Street, London EC3P 3DB, United Kingdom)

  • Peter Løchte Jørgensen

    ()

    (Department of Management, University of Aarhus, Building 350, DK-8000 Aarhus C, Denmark)

This article derives the first analytical pricing formulas for American-style Asian options of the so-called floating strike type. Geometric as well as arithmetic averaging is considered. The setup is a standard Black-Scholes framework where the price of the underlying security evolves according to a geometric Brownian motion. A decomposition result that splits up the value of the floating strike American option into the price of an otherwise equivalent European option and an early exercise premium is first presented. This decomposition result is then manipulated further for the two separate types of averaging. With geometric averaging we derive an exact pricing formula, whereas with arithmetic averaging we develop an analytical approximation formula that proves to be very precise. Numerical examples are provided.

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File URL: http://dx.doi.org/10.1287/mnsc.46.8.1116.12027
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Article provided by INFORMS in its journal Management Science.

Volume (Year): 46 (2000)
Issue (Month): 8 (August)
Pages: 1116-1136

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Handle: RePEc:inm:ormnsc:v:46:y:2000:i:8:p:1116-1136
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  1. S. D. Jacka, 1991. "Optimal Stopping and the American Put," Mathematical Finance, Wiley Blackwell, vol. 1(2), pages 1-14.
  2. Peter Ritchken & L. Sankarasubramanian & Anand M. Vijh, 1993. "The Valuation of Path Dependent Contracts on the Average," Management Science, INFORMS, vol. 39(10), pages 1202-1213, October.
  3. Kemna, A. G. Z. & Vorst, A. C. F., 1990. "A pricing method for options based on average asset values," Journal of Banking & Finance, Elsevier, vol. 14(1), pages 113-129, March.
  4. 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(03), pages 377-389, September.
  5. Milevsky, Moshe Arye & Posner, Steven E., 1998. "Asian Options, the Sum of Lognormals, and the Reciprocal Gamma Distribution," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 33(03), pages 409-422, September.
  6. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
  7. Peter Carr & Robert Jarrow & Ravi Myneni, 2008. "Alternative Characterizations Of American Put Options," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 5, pages 85-103 World Scientific Publishing Co. Pte. Ltd..
  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 177-86, March.
  9. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
  10. Levy, Edmond, 1992. "Pricing European average rate currency options," Journal of International Money and Finance, Elsevier, vol. 11(5), pages 474-491, October.
  11. Bouaziz, Laurent & Briys, Eric & Crouhy, Michel, 1994. "The pricing of forward-starting asian options," Journal of Banking & Finance, Elsevier, vol. 18(5), pages 823-839, October.
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