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Computational Economics

, Volume 53, Issue 1, pp 259–287 | Cite as

Radial Basis Functions with Partition of Unity Method for American Options with Stochastic Volatility

  • Reza MollapouraslEmail author
  • Ali Fereshtian
  • Michèle Vanmaele
Article

Abstract

In this article, we price American options under Heston’s stochastic volatility model using a radial basis function (RBF) with partition of unity method (PUM) applied to a linear complementary formulation of the free boundary partial differential equation problem. RBF-PUMs are local meshfree methods that are accurate and flexible with respect to the problem geometry and that produce algebraic problems with sparse matrices which have a moderate condition number. Next, a Crank–Nicolson time discretisation is combined with the operator splitting method to get a fully discrete problem. To better control the computational cost and the accuracy, adaptivity is used in the spatial discretisation. Numerical experiments illustrate the accuracy and efficiency of the proposed algorithm.

Keywords

Radial basis function Partition of unity Operator splitting American option pricing Stochastic volatility Heston’s model 

Notes

Acknowledgements

The first author would like to thank the Department of Applied Mathematics, Computer Science and Statistics of Ghent University and the FWO Scientific Research Network Stochastic Modelling with Applications in Financial Markets for some financial support during his scientific research stay at that department. The authors thank professor in ’t Hout for some fruitful discussion.

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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  • Reza Mollapourasl
    • 1
    • 3
    Email author
  • Ali Fereshtian
    • 1
  • Michèle Vanmaele
    • 2
  1. 1.School of MathematicsShahid Rajaee Teacher Training UniversityLavizan, TehranIran
  2. 2.Department of Applied Mathematics, Computer Science and StatisticsGhent UniversityGhentBelgium
  3. 3.Department of MathematicsOregon State UniversityCorvallisUSA

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