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Chebyshev polynomial approximation to approximate partial differential equations

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Author Info
Guglielmo Maria Caporale
Mario Cerrato

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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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Publisher Info
Paper provided by Department of 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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Postal: Adam Smith Building, University of Glasgow, Glasgow G12 8RT
Phone: 0141 330 4618
Fax: 0141 330 4940
Web page: http://www.gla.ac.uk/departments/economics/
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Related research
Keywords: European Options; Chebyshev Polynomial Approximation; Chebyshev Nodes;

Find related papers by JEL classification:
C63 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Computational Techniques
G12 - Financial Economics - - General Financial Markets - - - Asset Pricing

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  1. 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. [Downloadable!]
  2. 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. [Downloadable!]
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This page was last updated on 2009-12-8.

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