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The critical stock price for the American put option

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  • Chung, Y. Peter
  • Johnson, Herb
  • Polimenis, Vassilis

Abstract

We derive a simple relationship between the critical stock price and the gamma of the American put. We use this relationship to derive the correct expression for the critical stock price as time to maturity goes to zero and an analytic approximation for the in-the-money American put price. We present simple, analytical expressions for the critical stock price.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:finlet:v:8:y:2011:i:1:p:8-14
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    References listed on IDEAS

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    1. 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.
    2. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    3. Nunes, João Pedro Vidal, 2009. "Pricing American Options under the Constant Elasticity of Variance Model and Subject to Bankruptcy," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 44(5), pages 1231-1263, October.
    4. Cox, John C. & Ross, Stephen A., 1976. "The valuation of options for alternative stochastic processes," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 145-166.
    5. Etienne Chevalier, 2005. "Critical Price Near Maturity For An American Option On A Dividend‐Paying Stock In A Local Volatility Model," Mathematical Finance, Wiley Blackwell, vol. 15(3), pages 439-463, July.
    6. Gao, Bin & Huang, Jing-zhi & Subrahmanyam, Marti, 2000. "The valuation of American barrier options using the decomposition technique," Journal of Economic Dynamics and Control, Elsevier, vol. 24(11-12), pages 1783-1827, October.
    7. Guy Barles & Julien Burdeau & Marc Romano & Nicolas Samsoen, 1995. "Critical Stock Price Near Expiration," Mathematical Finance, Wiley Blackwell, vol. 5(2), pages 77-95, April.
    8. 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.
    9. David S. Bunch & Herb Johnson, 2000. "The American Put Option and Its Critical Stock Price," Journal of Finance, American Finance Association, vol. 55(5), pages 2333-2356, October.
    10. Peter Carr & Robert Jarrow & Ravi Myneni, 2008. "Alternative Characterizations Of American Put Options," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 5, pages 85-103, World Scientific Publishing Co. Pte. Ltd..
    11. Marek Rutkowski, 1994. "The Early Exercise Premium Representation Of Foreign Market American Options1," Mathematical Finance, Wiley Blackwell, vol. 4(4), pages 313-325, October.
    12. S. D. Jacka, 1991. "Optimal Stopping and the American Put," Mathematical Finance, Wiley Blackwell, vol. 1(2), pages 1-14, April.
    13. 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.
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    Cited by:

    1. Liu, Yanchu & Cui, Zhenyu & Zhang, Ning, 2016. "Integral representation of vega for American put options," Finance Research Letters, Elsevier, vol. 19(C), pages 204-208.

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