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Chebyshev polynomial approximation to approximate partial differential equations

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  • Guglielmo Maria Caporale
  • Mario Cerrato

Abstract

This pa per suggests a simple method based on Chebyshev approximation at Chebyshev nodes to approximate partial differential equations. The methodology simply consists in determining the value function by using a set of nodes and basis functions. We provide two examples. Pricing an European option and determining the best policy for chatting down a machinery. The suggested method is flexible, easy to program and efficient. It is also applicable in other fields, providing efficient solutions to complex systems of partial differential equations.

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File URL: http://www.gla.ac.uk/media/media_80231_en.pdf
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Bibliographic Info

Paper provided by Business School - Economics, University of Glasgow in its series Working Papers with number 2008_16.

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Date of creation: Mar 2008
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Handle: RePEc:gla:glaewp:2008_16

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Related research

Keywords: European Options; Chebyshev Polynomial Approximation; Chebyshev Nodes;

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  1. Lars Stentoft, 2004. "Assessing the Least Squares Monte-Carlo Approach to American Option Valuation," Review of Derivatives Research, Springer, vol. 7(2), pages 129-168, 08.
  2. Abadir, Karim M. & Rockinger, Michael, 2003. "Density Functionals, With An Option-Pricing Application," Econometric Theory, Cambridge University Press, vol. 19(05), pages 778-811, October.
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