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Evaluation of a least-squares radial basis function approximation method for solving the Black-Scholes equation for option pricing
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology.
2012 (English)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
Abstract [en]

Radial basis function (RBF) approximation, is a new extremely powerful tool that is promising for high-dimensional problems, such as those arising from pricing of basket options using the Black-Scholes partial differential equation. The main problem for RBF methods have been ill-conditioning as the RBF shape parameter becomes small, corresponding to flat RBFs. This thesis employs a recently developed method called the RBF-QR method to reduce computational cost by improving the conditioning, thereby allowing for the use of a wider range of shape parameter values.

Numerical experiments for the one-dimensional case are presentedĀ  and a MATLAB implementation is provided. In our thesis, the RBF-QR method performs betterĀ  than the RBF-Direct method for small shape parameters. Using Chebyshev points, instead of a standard uniform distribution, can increase the accuracy through clustering of the nodes towards the boundary. The least squares formulation for RBF methods is preferable to the collocation approach because it can result in smaller errorsĀ  for the same number of basis functions.

Place, publisher, year, edition, pages
2012.
Series
IT, 12 051
Keyword [en]
RBF, radial basis function, ill-conditioning, shape parameter, Black-Scholes equation, option pricing
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:uu:diva-183042OAI: oai:DiVA.org:uu-183042DiVA: diva2:561754
Educational program
Master Programme in Computational Science
Uppsok
Technology
Supervisors
Examiners
Available from: 2012-10-22 Created: 2012-10-22 Last updated: 2012-10-22Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
  • ieee
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  • de-DE
  • en-GB
  • en-US
  • fi-FI
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Output format
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