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Comparison of numerical and analytical approximations of the early exercise boundary of the American put option

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  • Martin Lauko
  • Daniel Sevcovic

Abstract

In this paper we present qualitative and quantitative comparison of various analytical and numerical approximation methods for calculating a position of the early exercise boundary of the American put option paying zero dividends. First we analyze their asymptotic behavior close to expiration. In the second part of the paper, we introduce a new numerical scheme for computing the entire early exercise boundary. The local iterative numerical scheme is based on a solution to a nonlinear integral equation. We compare numerical results obtained by the new method to those of the projected successive over relaxation method and the analytical approximation formula recently derived by Zhu.

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  • Martin Lauko & Daniel Sevcovic, 2010. "Comparison of numerical and analytical approximations of the early exercise boundary of the American put option," Papers 1002.0979, arXiv.org, revised Aug 2010.
    • Handle: RePEc:arx:papers:1002.0979
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    Cited by:

    1. Soren Christensen, 2011. "A method for pricing American options using semi-infinite linear programming," Papers 1103.4483, arXiv.org, revised Jun 2011.
    2. Denis Veliu & Roberto De Marchis & Mario Marino & Antonio Luciano Martire, 2022. "An Alternative Numerical Scheme to Approximate the Early Exercise Boundary of American Options," Mathematics, MDPI, vol. 11(1), pages 1-12, December.
    3. Anna Clevenhaus & Matthias Ehrhardt & Michael Günther & Daniel Ševčovič, 2020. "Pricing American Options with a Non-Constant Penalty Parameter," JRFM, MDPI, vol. 13(6), pages 1-7, June.
    4. Jose Cruz & Daniel Sevcovic, 2020. "On solutions of a partial integro-differential equation in Bessel potential spaces with applications in option pricing models," Papers 2003.03851, arXiv.org.
    5. Belssing Taruvinga, 2019. "Solving Selected Problems on American Option Pricing with the Method of Lines," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 4-2019.
    6. Luca Vincenzo Ballestra, 2018. "Fast and accurate calculation of American option prices," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 41(2), pages 399-426, November.
    7. Sören Christensen, 2014. "A Method For Pricing American Options Using Semi-Infinite Linear Programming," Mathematical Finance, Wiley Blackwell, vol. 24(1), pages 156-172, January.

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