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The simplest American and Real Option approximations: Geske-Johnson interpolation in maturity and yield


  • San-Lin Chung
  • Mark Shackleton


The American early exercise feature of the Real Option to invest in a new project is important in capital budgeting and project valuation. Closed form solutions for American, and therefore Real, Options are known for two special cases; an infinite horizon generates the Merton (Bell Journal of Economics, 4, 141-83, 1973) solution while a zero dividend yield on the project generates Black-Scholes (Journal of Political Economy, 81, 637-59, 1973) prices since early exercise is never optimal. Geske-Johnson (Journal of Finance, 39, 1511-24, 1984) approximation is extended to a bivariate case by assuming various forms of separability for option prices as a function of time to maturity and yield to produce fully explicit and asymptotically correct approximations. These methods are compared with another simple approximation method due to Barone-Adesi and Whaley (Journal of Finance, 42, 301-20, 1987) and MacMillan (Advances in Futures Options and Research, 2, 117-42, 1987) and the estimated error these expressions contain compared to an accurate numerical benchmark technique.

Suggested Citation

  • San-Lin Chung & Mark Shackleton, 2003. "The simplest American and Real Option approximations: Geske-Johnson interpolation in maturity and yield," Applied Economics Letters, Taylor & Francis Journals, vol. 10(11), pages 709-716.
  • Handle: RePEc:taf:apeclt:v:10:y:2003:i:11:p:709-716
    DOI: 10.1080/1350485032000138980

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    References listed on IDEAS

    1. Johnson, H. E., 1983. "An Analytic Approximation for the American Put Price," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 18(01), pages 141-148, March.
    2. Geske, Robert & Johnson, Herb E, 1984. " The American Put Option Valued Analytically," Journal of Finance, American Finance Association, vol. 39(5), pages 1511-1524, December.
    3. Barone-Adesi, Giovanni & Whaley, Robert E, 1987. " Efficient Analytic Approximation of American Option Values," Journal of Finance, American Finance Association, vol. 42(2), pages 301-320, June.
    4. 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 637-654, May-June.
    5. Ju, Nengjiu, 1998. "Pricing an American Option by Approximating Its Early Exercise Boundary as a Multipiece Exponential Function," Review of Financial Studies, Society for Financial Studies, vol. 11(3), pages 627-646.
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