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Confined exponential approximations for the valuation of American options

  • Jongwoo Lee
  • Dean Paxson
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    We provide an alternative analytic approximation for the value of an American option using a confined exponential distribution with tight upper bounds. This is an extension of the Geske and Johnson compound option approach and the Ho et al. exponential extrapolation method. Use of a perpetual American put value, and then a European put with high input volatility is suggested in order to provide a tighter upper bound for an American put price than simply the exercise price. Numerical results show that the new method not only overcomes the deficiencies in existing two-point extrapolation methods for long-term options but also further improves pricing accuracy for short-term options, which may substitute adequately for numerical solutions. As an extension, an analytic approximation is presented for a two-factor American call option.

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    Article provided by Taylor & Francis Journals in its journal The European Journal of Finance.

    Volume (Year): 9 (2003)
    Issue (Month): 5 ()
    Pages: 449-474

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    Handle: RePEc:taf:eurjfi:v:9:y:2003:i:5:p:449-474
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    1. 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.
    2. Geske, Robert & Johnson, Herb E, 1984. " The American Put Option Valued Analytically," Journal of Finance, American Finance Association, vol. 39(5), pages 1511-24, December.
    3. Bjerksund, Petter & Stensland, Gunnar, 1993. "Closed-form approximation of American options," Scandinavian Journal of Management, Elsevier, vol. 9(Supplemen), pages S87-S99.
    4. Blomeyer, Edward C. & Johnson, Herb, 1988. "An Empirical Examination of the Pricing of American Put Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 23(01), pages 13-22, March.
    5. Barone-Adesi, Giovanni & Whaley, Robert E, 1987. " Efficient Analytic Approximation of American Option Values," Journal of Finance, American Finance Association, vol. 42(2), pages 301-20, June.
    6. Gibson, Rajna & Schwartz, Eduardo S, 1990. " Stochastic Convenience Yield and the Pricing of Oil Contingent Claims," Journal of Finance, American Finance Association, vol. 45(3), pages 959-76, July.
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