Fourier and wavelet option pricing methods

Kees Oosterlee, Luis Ortiz-Gracia, Stefanus C. Maree

Research output: Chapter in Book/Conference proceedings/Edited volumeChapterScientific

1 Citation (Scopus)

Abstract

In this overview chapter, we will discuss the use of exponentially converging option pricing techniques for option valuation. We will focus on the pricing of European options, and they are the basic instruments within a calibration procedure when fitting the parameters in asset dynamics. The numerical solution is governed by the solution of the discounted expectation of the pay-off function. For the computation of the expectation, we require knowledge about the corresponding probability density function, which is typically not available for relevant stochastic asset price processes. Many publications regarding highly efficient pricing of these contracts are available, where computation often takes place in the Fourier space. Methods based on quadrature and the Fast Fourier Transform (FFT) [1-3] and methods based on Fourier cosine expansions [4,5] have therefore been developed because for relevant log-asset price processes, the characteristic function appears to be available. The characteristic function is defined as the Fourier transform of the density function. Here, we wish to extend the overview by discussing the recently presented highly promising class of wavelet option pricing techniques, based on either B-splines or Shannon wavelets.

Original languageEnglish
Title of host publicationHigh-Performance Computing in Finance
Subtitle of host publicationProblems, Methods, and Solutions
EditorsM.A.H. Dempster, J. Kanniainen, J. Keane, E. Vynckier
Place of PublicationBoca Raton
PublisherTaylor & Francis
Chapter8
Pages249-272
Number of pages24
Edition1st
ISBN (Electronic)978-1-4822-9967-0
ISBN (Print)978-1-4822-9966-3
Publication statusPublished - 2018

Publication series

NameChapman and Hall/CRC Financial Mathematics Series
PublisherTaylor and Francis Group

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  • Cite this

    Oosterlee, K., Ortiz-Gracia, L., & Maree, S. C. (2018). Fourier and wavelet option pricing methods. In M. A. H. Dempster, J. Kanniainen, J. Keane, & E. Vynckier (Eds.), High-Performance Computing in Finance: Problems, Methods, and Solutions (1st ed., pp. 249-272). (Chapman and Hall/CRC Financial Mathematics Series). Taylor & Francis. https://www.taylorfrancis.com/books/e/9781482299670/chapters/10.1201%2F9781315372006-8