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The Analytic Valuation of American Options

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  • Kim, In Joon

Abstract

No analytic solutions exists for the valuation of American options written on futures contracts and foreign currencies for which early exercise may be optimal. This article formulates the American option valuation problem in economically and mathematically meaningful ways. This enables us to derive valuation formulas for American options. The properties associated with the optimal exercise boundary are examined, and a numerical technique to implement the valuation formulas is presented. Article published by Oxford University Press on behalf of the Society for Financial Studies in its journal, The Review of Financial Studies.

Suggested Citation

  • Kim, In Joon, 1990. "The Analytic Valuation of American Options," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 547-572.
  • Handle: RePEc:oup:rfinst:v:3:y:1990:i:4:p:547-72
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    Citations

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    Cited by:

    1. Andrew Ziogas & Carl Chiarella, 2003. "McKean’s Method applied to American Call Options on Jump-Diffusion Processes," Computing in Economics and Finance 2003 39, Society for Computational Economics.
    2. Rachel Kuske & Joseph Keller, 1998. "Optimal exercise boundary for an American put option," Applied Mathematical Finance, Taylor & Francis Journals, vol. 5(2), pages 107-116.
    3. Carl Chiarella & Andrew Ziogas, 2006. "American Call Options on Jump-Diffusion Processes: A Fourier Transform Approach," Research Paper Series 174, Quantitative Finance Research Centre, University of Technology, Sydney.
    4. B. Gao J. Huang, "undated". "The Valuation of American Barrier Options Using the Decomposition Technique," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-002, New York University, Leonard N. Stern School of Business-.
    5. Jérôme B. Detemple & Carlton Osakwe, 1999. "The Valuation of Volatility Options," CIRANO Working Papers 99s-43, CIRANO.
    6. Manuel Moreno & Javier Navas, 2003. "On the Robustness of Least-Squares Monte Carlo (LSM) for Pricing American Derivatives," Review of Derivatives Research, Springer, vol. 6(2), pages 107-128, May.
    7. Chiarella, Carl & Ziogas, Andrew, 2005. "Evaluation of American strangles," Journal of Economic Dynamics and Control, Elsevier, vol. 29(1-2), pages 31-62, January.
    8. Mark Broadie & Jérôme B. Detemple, 1996. "American Options on Dividend-Paying Assets," CIRANO Working Papers 96s-16, CIRANO.
    9. Denis Belomestny & Pavel V. Gapeev, 2006. "An Iteration Procedure for Solving Integral Equations Related to Optimal Stopping Problems," SFB 649 Discussion Papers SFB649DP2006-043, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    10. Pierangelo Ciurlia & Ilir Roko, 2005. "Valuation of American Continuous-Installment Options," Computational Economics, Springer;Society for Computational Economics, vol. 25(1), pages 143-165, February.
    11. Carl Chiarella & Adam Kucera & Andrew Ziogas, 2004. "A Survey of the Integral Representation of American Option Prices," Research Paper Series 118, Quantitative Finance Research Centre, University of Technology, Sydney.
    12. Roland Mallier & Ghada Alobaidi, 2000. "Laplace transforms and American options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 7(4), pages 241-256.
    13. Mark Broadie & Jérôme B. Detemple, 1996. "Recent Advances in Numerical Methods for Pricing Derivative Securities," CIRANO Working Papers 96s-17, CIRANO.

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