Using Chebyshev Polynomials to Approximate Partial Differential Equations

20 Pages Posted: 28 May 2008

See all articles by Guglielmo Maria Caporale

Guglielmo Maria Caporale

Brunel University London - Department of Economics and Finance; London South Bank University; CESifo (Center for Economic Studies and Ifo Institute); German Institute for Economic Research (DIW Berlin)

Mario Cerrato

London Metropolitan University - Department of Economics, Finance and International Business (EFIB)

Date Written: May 1, 2008

Abstract

This paper suggests a simple method based on a Chebyshev approximation at Chebyshev nodes to approximate partial differential equations. It consists of determining the value function by using a set of nodes and basis functions. We provide two examples: pricing a European option and determining the best policy for shutting down a machine. The suggested method is flexible, easy to programme and efficient. It is also applicable in other fields, providing efficient solutions to complex systems of partial differential equations.

Keywords: European options, Chebyshev polynomial approximation, Chebyshev nodes

JEL Classification: C63, G12

Suggested Citation

Caporale, Guglielmo Maria and Cerrato, Mario, Using Chebyshev Polynomials to Approximate Partial Differential Equations (May 1, 2008). CESifo Working Paper Series No. 2308. Available at SSRN: https://ssrn.com/abstract=1137852

Guglielmo Maria Caporale (Contact Author)

Brunel University London - Department of Economics and Finance ( email )

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London South Bank University ( email )

Centre for Monetary and Financial Economics
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CESifo (Center for Economic Studies and Ifo Institute)

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German Institute for Economic Research (DIW Berlin) ( email )

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Berlin, 10117
Germany

Mario Cerrato

London Metropolitan University - Department of Economics, Finance and International Business (EFIB) ( email )

Economics Subject Group, LMBS
London EC2M 6SQ, EC2M 6SQ
United Kingdom

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