Computational and Applied Mathematics

, Volume 37, Issue 3, pp 2381–2398 | Cite as

A two-grid penalty method for American options

  • Tatiana P. Chernogorova
  • Miglena N. Koleva
  • Radoslav L. Valkov


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.


Penalty method Finite difference Two-grid Newton method Maximum principle 

Mathematics Subject Classification

35R35 65M06 



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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Copyright information

© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2017

Authors and Affiliations

  • Tatiana P. Chernogorova
    • 1
  • Miglena N. Koleva
    • 2
  • Radoslav L. Valkov
    • 3
  1. 1.Department of Numerical Methods and AlgorithmsSofia UniversitySofiaBulgaria
  2. 2.Department of MathematicsRuse UniversityRuseBulgaria
  3. 3.Department of Mathematics and Computer ScienceUniversity of AntwerpAntwerpBelgium

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