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A two-grid penalty method for American options

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Abstract

In this paper we consider the pricing of American options, governed by a partial differential complementarity problem. The differential problem is first approximated by a semi-linear PDE using two distinct penalty approaches which are well known in computational finance. We then initiate the two-grid algorithm by solving the nonlinear problem on a coarse grid and further the linearized in the interpolated coarse-grid solution problem on a fine grid. By means of the maximum principle the algorithm is shown to be of fourth order convergence rate in space. Numerical experiments verify the presented two-grid approach where we draw some interesting conclusions.

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Acknowledgements

Authors would like to thank the anonymous reviewers for their valuable and constructive comments that greatly contributed to improve the quality of the paper.

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Authors and Affiliations

  1. Department of Numerical Methods and Algorithms, Sofia University, Sofia, Bulgaria

    Tatiana P. Chernogorova

  2. Department of Mathematics, Ruse University, Ruse, Bulgaria

    Miglena N. Koleva

  3. Department of Mathematics and Computer Science, University of Antwerp, Antwerp, Belgium

    Radoslav L. Valkov

Authors
  1. Tatiana P. Chernogorova
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  2. Miglena N. Koleva
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  3. Radoslav L. Valkov
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Corresponding author

Correspondence to Miglena N. Koleva.

Additional information

Communicated by Jorge Zubelli.

The first author is supported by the Bulgarian Fund of Sciences under Project FNI I 02/9-2014. This research is supported by the European Union under Grant Agreement Number 304617 (FP7 Marie Curie Action Project Multi-ITN STRIKE-Novel Methods in Computational Finance) and the Bulgarian National Fund of Science under Project I02/20-2014.

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Chernogorova, T.P., Koleva, M.N. & Valkov, R.L. A two-grid penalty method for American options. Comp. Appl. Math. 37, 2381–2398 (2018). https://doi.org/10.1007/s40314-017-0457-6

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  • DOI: https://doi.org/10.1007/s40314-017-0457-6

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