Pricing Early-Exercise and Discrete Barrier Options by Shannon Wavelet Expansions

33 Pages Posted: 20 Dec 2015 Last revised: 16 Aug 2016

See all articles by Stefanus Maree

Stefanus Maree

Center for Mathematics and Computer Science (CWI); University of Amsterdam - University Medical Center

Luis Ortiz-Gracia

University of Barcelona

Cornelis W. Oosterlee

Center for Mathematics and Computer Science (CWI)

Date Written: August 15, 2016

Abstract

We present a pricing method based on Shannon wavelet expansions for early-exercise and discretely-monitored barrier options under exponential Lévy asset dynamics. Shannon wavelets are smooth, and thus approximate the densities that occur in finance well, resulting in exponential convergence. Application of the Fast Fourier Transform yields an efficient implementation and since wavelet are local approximations, the domain boundary errors can be naturally resolved, which is the main improvement over existing methods.

Keywords: Shannon wavelets; Bermudan options; barrier options

JEL Classification: C63

Suggested Citation

Maree, Stefanus and Ortiz-Gracia, Luis and Oosterlee, Cornelis W., Pricing Early-Exercise and Discrete Barrier Options by Shannon Wavelet Expansions (August 15, 2016). Available at SSRN: https://ssrn.com/abstract=2705699 or http://dx.doi.org/10.2139/ssrn.2705699

Stefanus Maree (Contact Author)

Center for Mathematics and Computer Science (CWI) ( email )

P.O. Box 94079
Amsterdam, NL-1090 GB
Netherlands

University of Amsterdam - University Medical Center ( email )

Meibergdreef 9
Amsterdam, 1105
Netherlands

Luis Ortiz-Gracia

University of Barcelona ( email )

Diagonal, 690
08034 Barcelona
Spain

Cornelis W. Oosterlee

Center for Mathematics and Computer Science (CWI) ( email )

P.O. Box 94079
Amsterdam, NL-1090 GB
Netherlands

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