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Numerical evaluation of the critical price and American options

Author

Listed:
  • Walter Allegretto
  • Giovanni Barone-Adesi
  • Robert Elliott

Abstract

An approximate solution to the American put value is proposed and implemented numerically. Relaxation techniques enable the critical price to be determined with high accuracy. The method uses a modification of the quadratic approximation of MacMillan and Barone-Adesi and Whaley which gives an expression for the critical price. Numerical experimentation and iterative methods quickly provide highly accurate solutions.

Suggested Citation

  • Walter Allegretto & Giovanni Barone-Adesi & Robert Elliott, 1995. "Numerical evaluation of the critical price and American options," The European Journal of Finance, Taylor & Francis Journals, vol. 1(1), pages 69-78.
    • Handle: RePEc:taf:eurjfi:v:1:y:1995:i:1:p:69-78
    DOI: 10.1080/13518479500000009
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    References listed on IDEAS

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    1. Patrick Jaillet & Damien Lamberton & Bernard Lapeyre, 1990. "Variational inequalities and the pricing of American options," Post-Print hal-01667008, HAL.
    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. Barone-Adesi, Giovanni & Whaley, Robert E, 1987. "Efficient Analytic Approximation of American Option Values," Journal of Finance, American Finance Association, vol. 42(2), pages 301-320, June.
    4. Brennan, Michael J & Schwartz, Eduardo S, 1977. "The Valuation of American Put Options," Journal of Finance, American Finance Association, vol. 32(2), pages 449-462, May.
    5. Kim, In Joon, 1990. "The Analytic Valuation of American Options," The Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 547-572.
    6. S. D. Jacka, 1991. "Optimal Stopping and the American Put," Mathematical Finance, Wiley Blackwell, vol. 1(2), pages 1-14, April.
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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. 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;Associazione per la Matematica, vol. 27(1), pages 35-56, August.
    3. Frontczak, Robert & Schöbel, Rainer, 2009. "On modified Mellin transforms, Gauss-Laguerre quadrature, and the valuation of American call options," Tübinger Diskussionsbeiträge 320, University of Tübingen, School of Business and Economics.
    4. Barone-Adesi, Giovanni, 2005. "The saga of the American put," Journal of Banking & Finance, Elsevier, vol. 29(11), pages 2909-2918, November.
    5. Giacomo Morelli & Lea Petrella, 2021. "Option Pricing, Zero Lower Bound, and COVID-19," Risks, MDPI, vol. 9(9), pages 1-13, September.
    6. Roland Mallier & Ghada Alobaidi, 2000. "Laplace transforms and American options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 7(4), pages 241-256.
    7. Siu, Tak Kuen, 2016. "A self-exciting threshold jump–diffusion model for option valuation," Insurance: Mathematics and Economics, Elsevier, vol. 69(C), pages 168-193.

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