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Smoothing of initial conditions for high order approximations 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]

In this article the Finite Difference method is used to solve the Black Scholes equation. A second order and fourth order accurate scheme is implemented in space and evaluated. The scheme is then tried for different initial conditions. First the discontinuous pay off function of a European Call option is used. Due to the nonsmooth charac- teristics of the chosen initial conditions both schemes show an order of two. Next, the analytical solution to the Black Scholes is used when t=T/2. In this case, with a smooth initial condition, the fourth order scheme shows an order of four. Finally, the initial nonsmooth pay off function is modified by smoothing. Also in this case, the fourth order method shows an order of convergence of four. 

Place, publisher, year, edition, pages
2016. , 22 p.
Series
TVE, 16029 maj
Keyword [en]
Finite Differences, Computational Finance, Black Scholes
National Category
Other Computer and Information Science
Identifiers
URN: urn:nbn:se:uu:diva-302322OAI: oai:DiVA.org:uu-302322DiVA: diva2:957102
Educational program
Master Programme in Engineering Physics
Supervisors
Examiners
Available from: 2016-09-28 Created: 2016-09-01 Last updated: 2016-09-28Bibliographically approved

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fulltext(1524 kB)143 downloads
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CiteExportLink to record
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Citation style
  • apa
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