Valuing American Put Options Using Chebyshev Polynomial Approximation

London Metropolitan University Working Paper

23 Pages Posted: 2 Mar 2005

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: February 2005

Abstract

This paper suggests a simple valuation method based on Chebyshev approximation at Chebyshev nodes to value American put options. It is similar to the approach taken in Sullivan (2000), where the option's continuation region function is estimated by using a Chebyshev polynomial. However, in contrast to Sullivan (2000), the functional is fitted by using Chebyshev nodes. The suggested method is flexible, easy to program and efficient, and can be extended to price other types of derivative instruments. It is also applicable in other fields, providing efficient solutions to complex systems of partial differential equations. The paper also describes an alternative method based on dynamic programming and backward induction to approximate the option value in each time period.

Keywords: American put options, Bellman equation, Chebyshev polynomial approximation, Chebyshev nodes

JEL Classification: C63, G12

Suggested Citation

Caporale, Guglielmo Maria and Cerrato, Mario, Valuing American Put Options Using Chebyshev Polynomial Approximation (February 2005). London Metropolitan University Working Paper. Available at SSRN: https://ssrn.com/abstract=675883 or http://dx.doi.org/10.2139/ssrn.675883

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
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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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