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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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    File URL: http://arxiv.org/pdf/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. 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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