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Critical Stock Price Near Expiration

Author

Listed:
  • Guy Barles
  • Julien Burdeau
  • Marc Romano
  • Nicolas Samsoen

Abstract

We study the critical price of an American put option near expiration in the Black‐Scholes model. Our main result is an estimate for the difference P̄ (t)‐ K between the critical price at time t and the exercise price as t approaches the maturity of the option.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:mathfi:v:5:y:1995:i:2:p:77-95
    DOI: 10.1111/j.1467-9965.1995.tb00103.x
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    Citations

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    Cited by:

    1. Ziwei Ke & Joanna Goard, 2019. "Penalty American Options," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(02), pages 1-32, March.
    2. Jun Cheng & Jin Zhang, 2012. "Analytical pricing of American options," Review of Derivatives Research, Springer, vol. 15(2), pages 157-192, July.
    3. Broadie, Mark & Detemple, Jerome & Ghysels, Eric & Torres, Olivier, 2000. "Nonparametric estimation of American options' exercise boundaries and call prices," Journal of Economic Dynamics and Control, Elsevier, vol. 24(11-12), pages 1829-1857, October.
    4. 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.
    5. 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.
    6. Anna Battauz & Marzia De Donno & Janusz Gajda & Alessandro Sbuelz, 2022. "Optimal exercise of American put options near maturity: A new economic perspective," Review of Derivatives Research, Springer, vol. 25(1), pages 23-46, April.
    7. Damien Lamberton & Mohammed Mikou, 2013. "Exercise boundary of the American put near maturity in an exponential Lévy model," Finance and Stochastics, Springer, vol. 17(2), pages 355-394, April.
    8. Barone-Adesi, Giovanni, 2005. "The saga of the American put," Journal of Banking & Finance, Elsevier, vol. 29(11), pages 2909-2918, November.
    9. Song-Ping Zhu & Jing Zhang, 2012. "How should a convertible bond be decomposed?," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 35(2), pages 113-149, November.
    10. 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.
    11. Tiziano De Angelis & Damien Lamberton, 2024. "A probabilistic approach to continuous differentiability of optimal stopping boundaries," Papers 2405.16636, arXiv.org.
    12. Sergei Levendorskiĭ, 2022. "Operators and Boundary Problems in Finance, Economics and Insurance: Peculiarities, Efficient Methods and Outstanding Problems," Mathematics, MDPI, vol. 10(7), pages 1-36, March.
    13. Damien Lamberton, 2018. "On the binomial approximation of the American put," Papers 1802.05614, arXiv.org, revised Dec 2018.
    14. Andrew Ziogas & Carl Chiarella, 2004. "Pricing American Options on Jump-Diffusion Processes using Fourier-Hermite Series Expansions," Computing in Economics and Finance 2004 177, Society for Computational Economics.
    15. Minqiang Li, 2010. "A quasi-analytical interpolation method for pricing American options under general multi-dimensional diffusion processes," Review of Derivatives Research, Springer, vol. 13(2), pages 177-217, July.
    16. Anna Battauz & Marzia De Donno & Alessandro Sbuelz, 2015. "Real Options and American Derivatives: The Double Continuation Region," Management Science, INFORMS, vol. 61(5), pages 1094-1107, May.
    17. Xinfu Chen & John Chadam & Lishang Jiang & Weian Zheng, 2008. "Convexity Of The Exercise Boundary Of The American Put Option On A Zero Dividend Asset," Mathematical Finance, Wiley Blackwell, vol. 18(1), pages 185-197, January.
    18. Dariusz Gatarek & Juliusz Jabłecki, 2021. "Between Scylla and Charybdis: The Bermudan Swaptions Pricing Odyssey," Mathematics, MDPI, vol. 9(2), pages 1-32, January.
    19. Wenting Chen & Song-Ping Zhu, 2022. "On the Asymptotic Behavior of the Optimal Exercise Price Near Expiry of an American Put Option under Stochastic Volatility," JRFM, MDPI, vol. 15(5), pages 1-19, April.
    20. Mojtaba Hajipour & Alaeddin Malek, 2015. "Efficient High-Order Numerical Methods for Pricing of Options," Computational Economics, Springer;Society for Computational Economics, vol. 45(1), pages 31-47, January.
    21. Roland Mallier & Ghada Alobaidi, 2000. "Laplace transforms and American options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 7(4), pages 241-256.

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