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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.

Suggested Citation

  • Guglielmo Maria Caporale & Mario Cerrato, 2008. "Chebyshev polynomial approximation to approximate partial differential equations," Working Papers 2008_16, Business School - Economics, University of Glasgow.
    • Handle: RePEc:gla:glaewp:2008_16
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    References listed on IDEAS

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    1. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," The Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 113-147.
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    More about this item

    Keywords

    European Options; Chebyshev Polynomial Approximation; Chebyshev Nodes;
    All these keywords.

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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