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Discretization of the Dirac delta function for application in option pricing
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing.
2016 (English)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
Abstract [en]

This paper compares two different approximations of the Dirac deltafunction used in a Fokker-Planck equation. Both methods deal with the singularity problem in the initial condition. The Dirac delta approximation, constructed in MATLAB with a method derived by Tornberg and Engquist, was compared to an already given method Aït-Sahalia. The methods were implemented as the initial condition in the Fokker-Planck equation, e.g approximating a probability density function. In most cases Aït-Sahalia and Tornberg-Engquist were interchangeable. During specific circumstances one method was significantly more accurate than the other. Increasing the amount of time/spatial steps enhanced the differences in error while having less time/spatial steps made the difference in error converge. The Aït-Sahalia method produces slightly more accurate results in more cases.

Place, publisher, year, edition, pages
2016. , 45 p.
Series
TVE, 16 067 juni
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-297648OAI: oai:DiVA.org:uu-297648DiVA: diva2:942736
Educational program
Master Programme in Engineering Physics
Supervisors
Examiners
Available from: 2016-06-30 Created: 2016-06-26 Last updated: 2016-06-30Bibliographically approved

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CiteExportLink to record
Permanent link

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Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
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Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
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  • Other locale
More languages
Output format
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