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The American Put Option and Its Critical Stock Price

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  • David S. Bunch

    (Graduate School of Management, University of California, Davis,)

  • Herb Johnson

    (A. Gary Anderson Graduate School of Management, University of California, Riverside)

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    Abstract

    We derive an expression for the critical stock price for the American put. We start by expressing the put price as an integral involving first-passage probabilities. This approach yields intuition for Merton's result for the perpetual put. We then consider the finite-lived case. Using (1) the fact that the put value ceases to depend on time when the critical stock price is reached and (2) the result that an American put equals a European put plus an early-exercise premium, we derive the critical stock price. We approximate the critical-stock-price function to compute accurate put prices. Copyright The American Finance Association 2000.

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    Bibliographic Info

    Article provided by American Finance Association in its journal The Journal of Finance.

    Volume (Year): 55 (2000)
    Issue (Month): 5 (October)
    Pages: 2333-2356

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    Handle: RePEc:bla:jfinan:v:55:y:2000:i:5:p:2333-2356

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    Cited by:
    1. Allegretto, Walter & Lin, Yanping & Yang, Hongtao, 2002. "A novel approach to the valuation of American options," Global Finance Journal, Elsevier, vol. 13(1), pages 17-28.
    2. 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.
    3. 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.
    4. Honglin Wang & Fan Yu & Yinggang Zhou, 2013. "Rental Rates under Housing Price Uncertainty: A Real Options Approach," Working Papers 242013, Hong Kong Institute for Monetary Research.
    5. Chuang-Chang Chang & Jun-Biao Lin & Wei-Che Tsai & Yaw-Huei Wang, 2012. "Using Richardson extrapolation techniques to price American options with alternative stochastic processes," Review of Quantitative Finance and Accounting, Springer, vol. 39(3), pages 383-406, October.
    6. Li, Minqiang, 2009. "A Quasi-analytical Interpolation Method for Pricing American Options under General Multi-dimensional Diffusion Processes," MPRA Paper 17348, University Library of Munich, Germany.
    7. Song-Ping Zhu, 2006. "An exact and explicit solution for the valuation of American put options," Quantitative Finance, Taylor & Francis Journals, vol. 6(3), pages 229-242.
    8. Antonella Basso & Martina Nardon & Paolo Pianca, 2004. "A two-step simulation procedure to analyze the exercise features of American options," Decisions in Economics and Finance, Springer, vol. 27(1), pages 35-56, 08.
    9. Battauz, A. & Pratelli, M., 2004. "Optimal stopping and American options with discrete dividends and exogenous risk," Insurance: Mathematics and Economics, Elsevier, vol. 35(2), pages 255-265, October.
    10. Manuel Moreno & Javier R. Navas, 2001. "On the robustness of least-squares Monte Carlo (LSM) for pricing American derivatives," Economics Working Papers 543, Department of Economics and Business, Universitat Pompeu Fabra.
    11. Medvedev, Alexey & Scaillet, Olivier, 2010. "Pricing American options under stochastic volatility and stochastic interest rates," Journal of Financial Economics, Elsevier, vol. 98(1), pages 145-159, October.
    12. Song-Ping Zhu & Jing Zhang, 2012. "How should a convertible bond be decomposed?," Decisions in Economics and Finance, Springer, vol. 35(2), pages 113-149, November.
    13. Minqiang Li, Li, 2009. "Analytical Approximations for the Critical Stock Prices of American Options: A Performance Comparison," MPRA Paper 15018, University Library of Munich, Germany.
    14. Jun Cheng & Jin Zhang, 2012. "Analytical pricing of American options," Review of Derivatives Research, Springer, vol. 15(2), pages 157-192, July.

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