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Optimal exercise boundary for an American put option

Author

Listed:
  • Rachel Kuske
  • Joseph Keller

Abstract

The optimal exercise boundary near the expiration time is determined for an American put option. It is obtained by using Green's theorem to convert the boundary value problem for the price of the option into an integral equation for the optimal exercise boundary. This integral equation is solved asymptotically for small values of the time to expiration. The leading term in the asymptotic solution is the result of Barles et al. An asymptotic solution for the option price is obtained also.

Suggested Citation

  • 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.
  • Handle: RePEc:taf:apmtfi:v:5:y:1998:i:2:p:107-116 DOI: 10.1080/135048698334673
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    References listed on IDEAS

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    1. Kim, In Joon, 1990. "The Analytic Valuation of American Options," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 547-572.
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    Cited by:

    1. Daniel Sevcovic, 2007. "An iterative algorithm for evaluating approximations to the optimal exercise boundary for a nonlinear Black-Scholes equation," Papers 0710.5301, arXiv.org.
    2. Chung, Y. Peter & Johnson, Herb & Polimenis, Vassilis, 2011. "The critical stock price for the American put option," Finance Research Letters, Elsevier, vol. 8(1), pages 8-14, March.
    3. Hsuan-Ku Liu, 2013. "The Convexity of the Free Boundary for the American put option," Papers 1304.5337, arXiv.org, revised Apr 2017.
    4. Chung, San-Lin & Shih, Pai-Ta, 2009. "Static hedging and pricing American options," Journal of Banking & Finance, Elsevier, vol. 33(11), pages 2140-2149, November.
    5. Tomas Bokes & Daniel Sevcovic, 2009. "Early exercise boundary for American type of floating strike Asian option and its numerical approximation," Papers 0912.1321, arXiv.org.
    6. Roland Mallier & Ghada Alobaidi, 2000. "Laplace transforms and American options," Applied Mathematical Finance, Taylor & Francis Journals, pages 241-256.

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