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Analyzing Various Implementations of the Radial Basis Function Partition of Unity Method for Option Pricing in 3D
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology.
2024 (English)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
Abstract [en]

This study evaluates the Radial Basis Function Partition of Unity Method (RBF-PUM) for itsrobustness and suitability for solving PDEs in option pricing. The robustness was tested byexamining the relative error behavior across its input parameters. To increase accuracy and toreduce computational time, three modifications were tested. These changes consisted ofchanging the node layout to use clustered Halton nodes, least squares projection aspreprocessing, and adding linear polynomials. The study shows that RBF-PUM achieves robustresults, suggesting its applicability to other option pricing problems. Furthermore, using a Haltonnode layout proved to be beneficial for the accuracy when using a smaller amount of nodes.The original implementation was less accurate, but more stable as the amount of nodesincreased. Least squares projections and added polynomials offered minor accuracy gains butincreased computation time, often making the trade-off unfavorable.

Place, publisher, year, edition, pages
2024.
Series
IT ; kDV 24 026
National Category
Computer and Information Sciences Computational Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-536322OAI: oai:DiVA.org:uu-536322DiVA, id: diva2:1889557
Educational program
Bachelor Programme in Computer Science
Supervisors
Examiners
Available from: 2024-08-16 Created: 2024-08-15 Last updated: 2024-08-16Bibliographically approved

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Computer and Information SciencesComputational Mathematics

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CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf